Originally we had planned on putting in a drain in the center of the floor
and hooking it into the house drain system. However, according to the plumber
this would be quite expensive and complicated since we would need a separate
trap from the washer ...

Find a smarter plumber. The washer drain does indeed need a trap and that will
be conveniently installed just below floor level. More important, there needs
to be proper venting of the drain line (after the trap) into the vent stack.
This may be where your plumber has a problem since it could involve some clever
work that he does not know how to quote for a fair profit. Of course you need a
pan for emergency overflow probelms just for insurance, but this is part of
most washer installations these days anyhow. Good luck.

Joe