Hm, I can not complain about my banks handling.
Now, exchange rates did suck for quite some time with them.... then I complained one day loudly, and the gav me a signed agreement for negotiable rates.
Now when I have to exchange sizable amounts of money (around 10000 USD in value), I call their forex dealing desk and exchange that thorugh their forex dealers. Even with the really high spread they give me for that (delivery etc.), I am really satisfied with them. Now, happens I also run a business and we get a lot of foreign money in.... so, I have plenty of cash reserve, and just call them every two months or so to move some funds into local currency. Works like a charm, and I get quotes a spread based on the forex rate THAT PARTICULAR MOMENT. VERY convenient when the market is in strong moves, and the "official exchange rates" the bank has to quote daily have insane spreads due to the volatility. Mine stays low. (and that is how it started - in a market loosing 4%-5% exchange rate I got a spread lower than what I could exchange in cash on exchange shops - because the banks only create that daily).
Sending money - simple SWIFT transfer at the bank. Not that expensive - a LOT cheaper than Moneygram. Plus it is what broekers expect. You wont get a brokerage accept Paypal. Or a MoneyGra. They want incoming bank transfer FROM THE OWNDER OF THE BROKER ACCOUNT (same account name).