I'm pretty sure academic snobbery will exclude me from getting a job at an investment bank but am I wasting my time trying to find a prop firm that will hire me with 6 months independent trading under my belt?
You mention academic snobbery but that generally isn't the case - in some cases it might be a crude filter in other cases a quantitative undergrad is rather useful... if you don't at least have the basics of multivariable calculus, linear algebra that any Maths/Physics/Engineering grad will have then getting to grips with relevant statistical techniques isn't going to go so well. It really depends on the type of firm, what they do etc..
Some prop firms are into HFT, HFT pretty much lends itself to being a prop activity given the strategies often have limited capacity and rather high returns - this is probably not what you're after if you don't have significant technical skills to be a developer or academic background to be a researcher.
There are the options market makers, they still trade from the screen, though generally they'll look for a 2:1 degree or above as a filter... plenty of them aren't necessarily all that picky on the initial screening but will get you to sit a bunch of aptitude tests with a load of other candidates and will quickly cut out most candidates on the first test - if you're not quick at doing simple calculations in your head at speed then plenty of these firms will be a non starter for you.
Lastly, the sort of firm you're probably thinking of is often referred to as a trading arcade - problem you have here is that you're basically just over a decade or so too late for this - the HFT firms have made futures markets much more efficient and sucked up a lot of the low hanging fruit the traders at these sorts of firms used to rely on. There are also some of firms out there now that will claim to be trading firms and will be willing to sell you a training course - avoid them for obvious reasons!
How arcades used to work - typically they'd get a bunch of guys in in their 20s, mostly recent uni graduates, and sit people in front of a simulator for 8 weeks and if you were able to consistently make money then they'd let you trade live with 1 lot then scale up from there - invariably the software used was TT for trading/sim and CQG (usually shared between two people) for charts.
The training consisted of presentations from account managers from various software vendors and exchanges (you'd usually get some pens or a mug and some educational material from the exchange - the guy from the Montreal exchange gave us all a pot of maple syrup!) and in the week before trading on the sim we spent some time reading through various material from the Eurex and CME websites. We also had a few books to read and write reviews on (presumably to demonstrate we had read and understood them) and a couple of little projects to work on. Some basic training was also presented in house regarding economic releases, trading spreads etc.. Basically none of this training was any secret sauce that would lead you to trading riches - there is very little incentive for some senior trader to teach you exactly what he does and have you copy him - he might as well just increase his size instead. Essentially most of what you'd learn on such a training scheme you could learn for yourself at home.
Some arcades would have everyone trading say STIRs, others including the one I was at were far more flexible and would let you try various things on the sim(AEX, CAC, FTSE, EuroStoxx, Dax, Bund/Bobl, WTI/Brent etc..)... so long as you were consistent at it then you'd be able to go live.
You'd get a basic salary, but this was essentially a draw down from the account... so this is a cost that immediately starts to add up before you've even gone live and that you'll need to cover with your future trading profits. The sim is free but once you go live you're looking at a couple of grand in software costs per month, additional fees depending on the number of exchanges you need to add, a desk fee and the cost of your basic salary, only once you've made enough money to cover those costs can you start getting into the profit split, which if you're fully backed by the firm typically started at 50% and then scaled upwards in your favour at set increments.
These trading firms don't generally offer these sorts of deals any more - the reason why is obvious, most people can't make money like that any more... point and click trading of futures just isn't anywhere near as feasible as it was as the markets are so much more efficient. Surprisingly though a few people seemingly still make money and so there are still some clearing firms/arcades who will rent desks and might perhaps be interested in some sort of arrangement if you're able to demonstrate some track record - it certainly isn't profitable anymore though for them to take on a whole bunch of 20-somethings and let them loose on the markets as they used to while paying them a basic salary.
Just to comment on some things you've mentioned:
The training isn't much to get your hopes up about, you'll need to discover your own edges.
You mention wanting to earn 30-50k EUR, that sort of amount is barely going to cover your costs in an arcade.
You also mention having traded for 6 months, have taken a big loss and only the last month is profitable (though you're still at a loss overall) and somewhere else in the thread you mention that you've done 350 trades in that period - assuming these were evenly distributed then your last month where you believe things have changed you've perhaps got a sample of only 60 trades from which you're making that assertion... if you were scalping some futures market on a sim you might well make this many trades in a single day, I'm not sure you can really conclude much from it at all.
You mention trading FX, I'm assuming this is via some bucketshop where you're forced to cross their spread in order to trade? If you were trying to find out if you had some edge in intraday trading in order to perhaps go to some prop firm then having to cross that spread is likely going to present some serious problems for you. As another poster pointed out earlier in the thread for these types of 'prop firms'/trading arcades you'd generally be trading futures (or equities too in the case of US firms).
You mention moving to London - that could turn into an expensive waste of time, you don't know that you're profitable yet, if your plan is to build up this track record you're planning to build up then adding additional costs to that probably isn't a good idea. I'll again reiterate that this sort of intraday trading isn't so feasible these days, you've got no idea yet if you'll be profitable - most of the people who used to do it for a living a decade ago aren't anymore so chances are rather slim!
And back to what I mentioned at the start, supposing you find yourself in the unlikely position where you are consistently profitable over the course of 6 months when trading futures intraday, you might well find yourself in a position where it is preferable to simply carry on with what you're already doing rather than go to some arcade and add on various fixed costs + give up a profit split - then again benefiting from lower RT costs and access to funding could be preferable.
Anyway I realise this has turned into a bit of a wall of text but hopefully some of it may be useful or give you pause to think.
for the trading arcade type prop firms in London you'd generally need to trade futures - you're very, very unlikely to be successful at point and click trading of futures intraday unless you build a time machine and go back 15 years - lots of these firms have closed down for good reason!
you might possibly get a shot at an options market maker if you're good at aptitude tests, mental maths etc..
though generally for the other types of prop firms you'd probably need to go back to university - for anything involving systematic trading/HFT then relevant post grad degrees and/or significant technical skills are generally needed