$300 is very fair to do this very hard work. You're nuts not to pay to do it. Breaking out old tile with my chisel-hammer and carting it away is the hardest part of tiling, you should let them do it. Besides, if you have a 200 sq.ft. kitchen you can't be that needy to do it yourself That's a big kitchen. You must be rich! :-)
There is a skill and talent involved in not damaging walls, baseboard, doors, cabinets etc. You'd have $100 into renting a tool, and carting the tile away, and you'd risk costly damage you may cause, not being familiar with the tool. Also, the worst times I've ever gouged myself were times I was taking out tile. Much of the time the tile breaks, it shears, leaving an edge like a razor blade.
Spend $200 more and sit back sipping tea and watch the tileguy kill himself.
thetiler