And, dare I ask without sounding like a complete user, what would you use if you were only doing < $1000/month. Would a credit card processor even touch you or is it basically just paypal?
Paypal and Google Checkout are both good alternative options to look at. In some cases when you factor in all of the upstream credit card processing charges you'll even pay less.
This discussion is probably dead, but just in case:
Within the last year, I've been in the position of doing <$1k/month on a credit card processor, and it was actually a delightful experience. The company I originally worked with was bought/renamed or something and I haven't had to deal with them in quite a few months, but I can probably dig up a contact. Email me if you like.
We use Braintree and they're great. We're not doing $250k/mo yet but had no problems getting signed up with them back in May.
We also helped a partner company get setup with BT recently. They're doing < $50K a month IIRC.
Have not run into most of the problems mentioned in the OP.