95 cobra occasional hard starts

Another thing to check - especially if your car has been modified (with bigger fuel injectors). After 25 years it's hard to find a GT Mustang that someone hasn't tinkered with in some way. If larger injectors were installed, and a tune either not done or not done well, or an aftermarket "calibrated" MAF used instead of a tune. The computer can adjust fueling while the car is running for mildly up-sized injectors (24lb usually) and a "calibrated" MAF can get the fueling adjustments it makes closer to where they need to be so it has to do less adjusting. But there's a special table in the computer memory that determines how much fuel it gives while cranking that makes no adjustments. It just opens the injectors for a pre-determined amount of time assuming a set fuel-pressure and the stock-sized injectors. If you have larger injectors and that part of a tune wasn't adjusted, you'll have hard-starts when hot. When cold it's less noticeable as the fuel requirements are higher already and a little extra fuel just makes it start easier.

So... long story short, if you had not-enough-fuel-pressure or fuel-flow (bad pump, pressure regulator, fuel filter) you'd likely find it harder to start when it's cold than when it's hot. And since you verified the 39psi it pretty much means the pump is doing its job.

Brighter side (after all this theory and nonsense) is that it's easy to see if you have a too-much-fuel condition. Depress the pedal all the way to the floor before turning the key when the engine is hot. Counter-intuitively, this puts the car in "flood-clearing" mode and won't inject any fuel at all while cranking (just the bit it sprays while the pump primes). If it starts easily, then you may need a tune / chip to correct the problem (or just use flood-clear mode when you need to get it running when it's hot).

For you awareness, there's no fuel-pressure-return module in the 95 (fuel pressure is not computer-controlled). There's just the vacuum-actuated fuel pressure regulator and a one-way valve back to the pump. But as you verified fuel pressure stays steady, no issues there.

Another common problem on our GT's is a failing TFI (Ignition Module) or PIP (Distributor magnetic pickup). They tend to really act up when they get heat-soaked. They'll eventually get to where they stall the car altogether while running, and it won't restart until it cools off and then it's like nothing ever happened. You can see if your problem is ignition-related the next time it does this by checking for spark when it won't start.

But I'd start with trying to start the car with flood-clearing mode. Cheap and easy.

Edit: I just noticed you reported 39psi with vacuum hose detached, and 31psi with vacuum hose connected. That would be weird, it should be the other way around (vacuum decreases the fuel pressure using the regulator). Assuming just a typo, but if that's actually happening, you do have a pump / regulator problem.