* Kcole, many of the 4.5 liter v-8s (M117), which had a production run from about '72 to '80, had that problem; a lot of cranking on hot start with an eventual uneven, faltering start. Like classic vapor lock. If you look under the hood of any of the later aluminum v-8s, which superceded the 4.5, you'll find a fuel cooler (part of the AC suction hose) to combat exactly that problem. Unfortunately, I don't know of any way to retrofit one of the later fuel coolers to the earlier 4.5 cars.
* I'm assuming here that you've checked out all the obvious (less expensive) maintenance items; plugs, plug wires, compression test, and fuel pressure test (line, control and rest pressures). If the line pressure is off, you can shim the pressure regulator in the fuel distributor to bring it back into spec. An incorrect control pressure curve would call for a new control pressure regulator (aka warm-up regulator). A deficient rest pressure will often point to a leaking injector or a leaking 1-way valve at the fuel pump. The fuel pump 1-way outlet valve isn't expensive but a little tricky to replace. The injectors, with new seals, are more expensive and time consuming. Depending on your resources, any/all of the above parts should make a noticeable performance difference on an older car. But it may still not solve the hot start problem.
* The most expensive item (save the expensive stuff for last if you have a choice) is the fuel distributor. Your fuel injection system is the Bosch K-Jetronic system, which came in in '73 and replaced the initial D-Jetronic system. I currently have a client with a very nice '78 450SLC with the same hot start problem. He's had all the other work and the car runs really well but is a pain to start hot. But he's living with it rather than buy a new fuel distributor.
* Partially blocked cats would give you a starting problem, hot or cold, but it wouldn't hurt to have a shop measure back pressure and verify that they're clear. Similarly, a clogged fuel filter won't differentiate between hot or cold, but is a routine maintenance item.
* If you're getting the sense that you could spend a lot of money chasing this problem and never really solve it completely, you're right. But good luck minimizing it.
* I look forward to reading anyone's account who has solved this problem completely.