Or better still use a router and those circular plastic inserts that fit
flush and take the routed out piece

I do have one of these and they are very good in some circumstances,
but a) the hole is circular and b) it's quite small. I want to cut a
hatch about 2' x 3'.

How about pinning a batten to the floor as a guide, using the router
with the thinnest straight cutter to cut an oblong hole (accurate and
easy to set depth of cut) and then adding battens to support the
cutout?