I am another Mustang/Shelby lover who is in favor of using the regular mechanical fuel pump unless you have a specialized fuel delivery system that requires a lot of pressure (fuel injection). I have only used replacement pumps from AutoZone, and in my case they have worked fine. But, the Carter M4009 having received the Jason and HemiKiller approval tells me it is a fine choice. The fuel pumps are not usually hard to replace, but if you have the fuel pump eccentric on the front of the camshaft timing gear in its "high" position you will be fighting with the pressure on the pump's actuating lever all the way. It is better to bump the engine a little at a time until the pump eccentric inside the timing case is in a "low" position, which takes all pressure off the actuating arm.
As for the pump's diaphragm having a leak, here is something I feel you should be aware of. When the fuel pump's diaphragm begins to leak there are two places the fuel can go, and in both cases it no longer goes where it should be going (carburetor fuel bowl after passing through the fuel filter before the carburetor). Either wrong place where fuel can go is bad, both is worse. One bad place for it to go is when it begins to pour liquid gasoline onto the ground. First, it is a fire risk, and when the external leak is "minimal" it wastes fuel.
The 2nd place it can go is into the engine crankcase. This is rather insidious as unless you know how to ascertain there is gasoline being leaked into the crankcase a person can be blissfully unaware the gasoline is contaminating the engine oil, and preventing the oil from properly protecting the inside normally lubricated surfaces of the many engine parts. The way I test to see if gasoline has invaded the crankcase is to pull the engine oil dipstick and simply sniff. If I detect even a hint of gasoline I know I better be changing the oil and filter. In my case personally I only sniff to see if it is evident there has been fuel contamination. Despite what I do or don't smell I always opt to change the oil and filter anyway just in case any occurred but I was not able to detect it. Call it cheap insurance.
It is also possible a leaking fuel pump can both leak externally, and into the crankcase. This is no time to make assumptions and overlook the potential for fuel contamination inside the engine. Fuel contaminated oil is capable of letting an engine become needlessly destroyed if the oil and filter are not changed.
Personally, I feel with these older cars the rubber fuel hoses at the fuel pump and fuel tank ought to be changed when the pump is changed, as it is likely what you have are the original fuel hose. And, unless you KNOW the fuel filter and rubber fuel filter hose are fairly new the fuel filter rubber hose ought to be replaced also. I change fuel filters and its rubber hose with every tuneup, every 2-3 years. Too often I have seen under-hood fires caused by a fuel filter's rubber hose becoming cracked and leaking liquid fuel really close the ignition distributor. When that happens those folks who are insured are the ones where the car it totaled. The less fortunate ones are those with no such insurance, or those with insurance where the car is not totaled. I have done a lot of those under-hood fire jobs in the past, and it is never pretty. The insurance adjusters would ask me to installed used parts from a wrecking yard, or to just "clean up" items scorched by the fire, then use graphite spray to over any discoloration, etc. More than once I had to tell an adjuster that a threat of never future under-hood fires to our dealership would be fine as I am paid "straight time," which costs me opportunity income as compared to be pad on a flat-rate basis, and I would also be relieved of having to deal with "someone" (adjuster) who is pressuring me to do a job on the cheap, as opposed to doing it correctly. I would also let the adjusters who pressured me know their little threats of moving the job at hand to a different shop was not going to intimidate me as in California the customer was able to select the shop doing the repairs, and if they persuaded a customer to have the job moved elsewhere I would be happy to let them know why it is their insurance company wanted to move it somewhere else. For the record, when I cleaned up an under-hood fire I did it right. Using new parts, and anything that was scorched got hot enough to require replacement even it is was apparently working at the time (alternators, for instance).
If you have not yet begun to replace the fuel pump, and the rubber fuel lines at the pump and fuel tank, Lynda and I made a YouTube video showing how to do it, kind of. I say "kind of" because there is a section, the actual pump replacement itself, where I thought the iPhone was in record mode, and it was off. But, there is enough content with the rest of the work to make watching it worth the time - IMHO. The engine in the Mustang where the fuel pump was replaced is a 302, which is essentially the same as a 351W. But, the 351C has a slightly different pump mount bolt orientation/pattern - otherwise everything else is the same. Here are the YouTube video links:
Rubber fuel line replacement at the fuel pump and fuel tank:
Preparing the new pump and gasket for installation:
Removing the fuel pump:
As explained above, the video showing how the new fuel pump was installed is missing due to an OFU (Operator Error) with the iPhone.
The complete set of the above videos in a single file: