There have been many HC owners solve various cranking issues with new batteries as the others have stated, but you can also properly test batteries so you know and are not guessing.
There are some good comments from other members in this thread. You mention that your voltage is at 13.8v, but that is with the engine running I believe?? 13.8v may indicate your alternator is good, but with the engine running at 1,500 RPM with a voltmeter hooked up, turn on the headlights, blower on high and rear defroster on...what is the voltage?? This will give you a great indication of alternator performance.
There are other battery checks that should be done before the running voltage is noted.
The battery has to have an open circuit (no load) voltage of 12.4v and stable (not decreasing).
Then, perform a battery load test. The load test should be 1/2 the CCA Rating for 15 seconds. Voltage should not drop below 9.6v during this test. Recharge the battery after this test.
Do a starter draw test. Crank the engine for 15 seconds (engine should not start; press accelerator all the way to the floor and hold while cranking; this prevents the engine from starting). Typical starter amperage draw is 200 to 250 amps. Battery voltage during test is usually around 10.5 volts during the test, but should never go below 9.6v. You can also see what voltage the alternator is putting out to recharge the battery after this cranking test, usually around 14.1 or .2 volts.
What is the cranking RPM?? You said your engine cranks strong, but what is the actual RPM and is it consistent during cranking?? North of 200 RPM??
There is a positive and negative side of the battery and all circuits. Both have to have good, clean and tight connections. The above tests will most likely vet these connections, but never assume anything.
If the above tests are good, what is the
fuel pressure during cranking?? Steady fuel pressure has to always be available for the engine to start. Our HCs do have fuel pump relays and there have been some cars with bad or poorly connected fuel pump relays on their cars.
Lastly, these engines have sensors inputs the PCM needs to see before the engine will fire, i.e. Crank and Cam position sensors. Techs need to know which sensor inputs are required and how to test for them.
You commented your car has had two starters replaced. This is just throwing parts at a car and it appears did not fix the issues.
Hope some of this helps...
Best!