Replacing the fuel pump likely won't get you anywhere — it's doing what it's supposed to do, generating pressure in the line from the pump to the carb. The claim was made in '73 that newly that year, slant-6 fuel pumps had an inbuilt bleed-down path to relieve line pressure after engine shutdown, but I've never seen a slant-6 pump (factory or aftermarket) that actually had any such a function. Then again, the same "What's new for '73" engineering bulletin also claimed the newly-redesigned slant-6 fuel pump also had a screw-in fuel filter in the outlet tower. Haven't seen one of those, either. Guess neither change made it past the bean counters. The internal bleed-down might've been a good idea, had they implemented it, but they found other ways to achieve the same result.
There was a TSB and "Flood-Stop" kit released in '68 to alleviate an overpressure condition in the line from the pump to the carb after engine shutdown. It consisted of two brass fittings. One threaded into the fuel pump outlet ahead of the pump-to-carb line, and the other spliced into the flexible hose between the frame line and the fuel pump inlet. Each of these fittings had a tiny pinhole at the end of a small hose nipple off the side of the fitting body. A short length of hose connected the two pinholed nipples. This provided a very low volume controlled "leak" from the pressure to the suction side of the pump. Not nearly enough ever to starve the engine for fuel, but enough so that when the engine was shut down the excess pressure in the pump-to-carb line would be bled off. Later, the 3-nipple fuel filter (5/16" inlet and outlet and a 1/4" vapour return nipple) was introduced for much the same purpose, but the return line was run all the way back to the tank. The flood-stop kit is long since NLA, but the 3-nipple filter is readily available. You can install one if it becomes necessary, but you'll have to figure out how to plumb the return line. Not too difficult, just a hassle.
As a first step, do the fuel line mod to minimise heat transfer to the fuel between the pump and the carb, and make sure you have the correct base gasket between the carb and the manifold. It should be 5/16" to 3/8" thick, not the 1/8" thin one. Also make sure your "heat riser" (manifold heat control valve) is working correctly. And yes, you do need to make sure the carb float and carb bowl vent plate are set correctly.
But, having said all that, it sounds like your setup's behaviour might not be too abnormal. Remember, the pre-'70 (California) pre-'71 (49-state/Canada) vehicles had the carburetor vented directly to the atmosphere, so yeah, when you park the vehicle with a hot engine, you're going to smell gasoline...especially with today's more odiferous gasoline/alcohol blends. If you're getting evidence of liquid gasoline running up overtop of the carb via the accelerator pump hole/bowl vent and dripping down onto the manifold below, then yeah, you definitely need to do some work to correct it. The "sounds like something dripping/leaking" effect, if you don't see any such external liquid fuel dripping, is usually fuel dripping from the nozzles inside the carb and hitting the hot throttle plate/manifold. Remove the air cleaner and take a look.
If you want to solve the problem "all the way solved" so you don't smell fuel, you can install a '70+ (California) '71+ (49-state/Canada) carburetor and put together a fuel vapour canister system as was done on '72-up models. It's not too difficult. Or you could park the truck outside!
