Yes, eliminate the check valve. They can easily disable one of the most
important safety devices on your boat as you have discovered. They serve no
useful purpose on a pump that pushes the water out unless your hose to sump
volume ratio is such that the water flooding back down the hose when the
pump stops will reactivate the float switch and send the system into an
endless cycle that runs down the battery. Even in that case, no check valve
sucking up the stuff that floats around in bilges can be relied upon to stay
tight. It will still cycle, just slower. There are also significant head
losses through the check valve the reduce the amount of water the pump can
move.

If you are having cycling problems, the vented loop Bob suggests can reduce
the hose volume if you get the loop close enough to the pump.

I do have a check valve on my diaphram hand pump just because it makes it
easier to get it primed and started. It's the rubber flap valve from extra
parts for the same Guzzler pump bolted together and inserted in the end of
the hose. If it jambs, I can just pull up the hose and stick my finger in
to clear the clog or yank the check valve out.

Check valves have no place in a bilge line other than right at end of the
inlet hose.

As to why the old valve worked and the new one doesn't, welcome to the new
world order of Chinese manufacturing domination. Don't bother returning it
for another just like it.

--
Roger Long