Some answers to your questions...
This Mercruiser 140 engine has the automatic choke (exhaust gas temperature controlled, not electric).
The choke flap was open when I had trouble starting the engine on Sunday afternoon. I had taken the spark arrestor can off the carb so I could check both the choke flapper and the accelerator plate down in the carb, to be sure both were open. When I had trouble at the resort several weeks ago, I did the same and the choke flapper was open then too.
I have not checked the timing. I bought a timing light earlier this summer, but have not hooked it up, because the engine was starting and running fine.
What should I look for? Wild variation between cold and hot?
In June, I had the carb totally disassembled, ultrasonically cleaned and rebuilt by The Carburator Shop in Maplewood. They have a 90 day warranty on their work. Should I pull the carb and ask them to check it again?
The starter seemed to be cranking at normal speed. The starter was replaced when the engine was installed in my boat in fall 2014. Could it have gone bad that quickly?
I don't recall having this hot-start problem last summer (the first summer after the Mercruiser 140 engine replacement). Last summer it was the opposite - hard to start when cold, due to the bad accelerator pump section of the carburetor.
Things that were changed since last summer:
1. replacement carb in fall 2015, to fix the accelerator pump fiasco
2. inline fuel filter (clear plastic) added, to be sure only clean fuel was getting to the carb, and so I could see that fuel was pumping. Adding this made the fuel line about 6 inches longer and so it touches the engine in a couple of places. (see photos).
3. Pertronix ignition coil added this summer. I have a Pertronix electronic ignition module (bought in fall 2013 for the previous engine and moved to this engine) in the current distributor cap and I was advised to get a matching Pertronix "Flamethrower" ignition coil to go with it. Could it be bad?
Could this be vapor lock?
Will a fuel pressure gauge reveal a vapor lock condition?
Earlier this summer I bought a pressure gauge that is purported to work as a fuel pressure gauge and a carb vacuum gauge.
https://www.amazon.com/gp/product/B00KRJFSFQ/ref=oh_aui_detailpage_o02_s00?ie=UTF8&psc=1To check for spark when it's hot, I could order one of these inline spark checkers?
https://www.amazon.com/Pittsburgh-Inline-Ignition-Spark-Checker/dp/B00L1IC2W4/ref=sr_1_2?s=hi&ie=UTF8&qid=1472483025&sr=1-2&keywords=spark+checker