not sure if this helps any?

looking at the schematic i see the logic supply is 18.7 VAC CT

so 9.3VAC across pins 12 (the centre tap) & 11 and 9.3 VAC across pins 12 & 10.

both lines 10 and 11 are fused with 4A slow blows.

imo you should change C16 and C17, and assuming you did change C15.

the resistors you mention getting hot is normal, reading the guide by vid1900 is very helpful.

i don't personally believe the 5V regulator needs replacing as you have stated your readings in #1 being 5.05VDC

Have you replaced diodes D7 & D8 with 6A 400V ones, or higher?

IC5 a 6820/6821 is a peripheral interface for the solenoids

Does the game shut down in 'attract mode', like after it boots up, without starting a game?

also with the power off, check all your coil diodes, including flippers. make sure they don't move and are soldered firmly in place.

or if in doubt replace them all, just a suggestion.

okay with the game 'dead' what is the output from the 5V regulator?

what is your line voltage?

all good

the same way tested the 5VDC in your first post, pins 7, 8, 9 & 10 on 3J6, top right hand side connector on power supply board.

red probe on 7, 8, 9, or 10 and black probe on 11, 12, 13 or 14 with multi meter set DC volts minimum 20V

it's well worth the read, covers driver board options

https://pinside.com/pinball/forum/topic/vids-guide-to-bulletproofing-williams-system-6

and

https://pinwiki.com/wiki/index.php?title=Williams_System_3_-_7#Reducing_heat_by_replacing_the_TIP-42_lamp_drive_transistors_and_eliminating_the_27_ohm_current_limiting_resistors

you can also use #47 globes instead of #44's if you want that look