WTB Apple IIe HAL 342-0140-A

Theoretically it should be possible to make a replacement with a still available GAL chip like the Atmel ATF 22V10, possibly with some kind of socket adapter.  But new stocks of the official Apple chips haven't been readily available in years, and the MMI HAL chips haven't been made in years and even programmers that can handle them are not commonly available anymore.  The chips are rarely sold separately used.  Unfortunately the easiest way to get one is to buy a whole //e motherboard or a whole //e unit.

You need a chip programmer that can handle a GAL chip.  I have an older MiniPro TL866CS which can handle some of the GAL chips like the Lattice made ones, but unfortunately those were discontinued a few years ago and starting to get hard to find.  None of the inexpensive programmers I know of can handle the currently available Microchip/Atmel ATF 22V10 chips.  There is a DIY project to build a programmer for them however.  If you google for it you should be able to find it.  It does require some work to build and use however and there is some learning curve to be able to turn the equations file you posted into something that can be programmed too.  But if someone can figure it out that would be a good thing, since as I said, the original Apple parts are scarce.

Only an ATF16V8 is required, although I think there has been a software update for the TL866CS allowing it to program the ATF22V10.

Indeed I have quite a few ATF16V8 chips in DIP-20 package left over from my IIgs RAM expansion before I switched it to SMD components.

I can program an ATF16V8 with the right logic equations and send it to you... but there is one possible issue. I think the currently-available GAL chips like the ATF16V8 are quite a bit faster than the HAL used in the IIe. Check this figure from Understanding the Apple IIe:

IIe Timing Signal Propagation Delay

It suggests that the typical delay for the signals coming from the timing HAL is 14 nanoseconds, whereas the slowest currently-available PALs in "-15" speed grade have a clock-to-output delay of 10 nanoseconds maximum, typically maybe 7 nanoseconds. But it's worth trying.

I can program a GAL within a few days and send it to you if you pay for the shipping and we can see if it works.

The TL866 Plus and the original TL866 are different.  The newer version will program some chips the old one won't and vice-versa.