Given that my new timbers (I hesitate to call them joists, cos they
aren't!) are not a structural part of the house as such, I was going
to use much less substantial wood for them than the real joists;

You should calculate the dead load of your proposed timbers and floorboards
and ensure that this loading does not make the existing joists too small.
What is the span and dimensions of the existing joists?

Christian.