$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.