Snap! I got a PSX-40 for $5 too. Fine cart, but the P-adapter (all P-adapters) causes 2 problems:
1) Loss of rigidity.
2) Poor electrical contact — the cartridge pins are thin; they go into hollow tubes on the adapter, which have an OD that fits the normal-size headshell pins. But the internal contact (inside the tube) is not good, it's loose. It's an extra connection (causing a bit of signal loss) and it's a bad extra connection. I used contact-enhancer, but didn't help much.
I fix problem 1) by glueing the cart into the adapter. Now it's rigid. It can't be used in a P-mount arm anymore, but I don't have one so it doesn't matter. (Keep the little bolt in there while glueing, for clamping-action and alignment, then remove it to keep mass low).
I fix problem 2) by removing the hollow tubes, and connecting directly to the original pins. This means "crushing" the cartridge clips a bit to get a good tight fit on those thin pins.
The improvement isn't subtle, it's dramatic. A whole new cartridge, a much better cartridge.
I have to destroy an adapter ($10, worth it) and probably destroy a set of h'shell leads (I haven't tried opening the clips up again).
Totally worth it in my book. People pay 20-times more than that for a new cable hoping for just a slight improvement.