Cracked Flex Plate

I can't believe nobody recommended to do a pressure test at the low/reverse servo. You're looking for ~250psi or more at 1600rpm, in reverse. The spec is 230 to 300.
Reverse gear pressure is unregulated and shows max pump pressure. No sense pulling the trans swapping in a new pump, and then finding out nothing changed.
If the pressure is up at reverse, then your forward clutch may be hemorrhaging so off with the pan, off with the VB and air-pressure test is next. While the pan is off you can adjust the bands.

Did you re-connect your KD linkage?

But you know what; delayed engagement can also be low fluid lever or aerated fluid. Since you say it didn't do this before the flex-plate swap,and you say the fluid is properly checked and correct; I'd recommend to drive the car around the block a couple of times, to purge the air out of all the circuits, then recheck the fluid level. Top up as required, and recheck the engagement. If still delayed, I personally, would add a half a liter and see if anything changes. Why would I do this? Because 50 years is a long time for the dipstick to still be original, and all your clues point to aerated or a low fluid level.
If still delayed, THEN I would do the pressure tests.

BTW, I have never seen a convertor pull-ahead remotely close to 1/8. More often than not, it is over 1/4". IMO,There is plenty of machined flat on the pump-drive to accommodate that and I have never shimmed it down nor had a problem. Maybe I have always been lucky, IDK.