We have a heat pump. The compressor is outside; the air handler is
inside, in an unfinished attic. I.e., there is no flooring and access
is through a "hatch" reached by a ladder.

Every time someone goes up there, to service the air handler,
install an attic fan, etc., the heads of nails holding the ceiling to
the joists "pop" through the ceiling below, making a very noticeable
dimple in the paint, and occasionally breaking through. It's a real
drag having this happen every time someone goes up there.

Is there some way to prevent this from happening?

I thought that if I were able to floor part of the attic, i.e., the
areas where these servicemen need to walk in order to access the air
handler, might this spread the load somewhat and perhaps prevent these
dimples from forming every time they go up there?

If so, what thickness of particle board should I put down?

If folks think this won't do the trick, what might???

Many thanks,
Bob