It's amazing how tenaciously some people like to hang on to their ideas about how things used to be done. Using a programmed device isn't "cheating", it's simply how this kind of thing is done nowadays. Other than analogue functions (eg. 4052) and specialist I/O, I can't remember the last time I used a 74 series logic chip. The cost is all in the packaging, board space and assembly; what's actually inside that SO14 package really doesn't matter at all. (Add 10p for programming if you really want).
My original idea was two Schottky diodes into a cap into LM393 into 555, with a side car of a TL431. If I go the PIC route the LM393 and the 555 are gone, but the TL431 + pot reference circuit and the Schottky diode peak detector is still there.