Ok, so I have a Delta-issued ticket for a trip that contains three legs on Aeromexico (well, one of which is actually an Aeromexico codeshare with Mexicana, to make things even more screwy, but that's on an RJ, so it doesn't matter.) On at least one of the legs, I'm required to check in directly with the Aeromexico desk.

I'm Delta Silver and Aeromexico Club Premier Gold, so...

Should I switch my FF# on the ticket to my Aeromexico number in hopes that on the AM legs I'll get upgraded to Clase Premier? Or will flashing my card at the check-in desk, while still having my Delta number attached to the tickets, accomplish the same goal? Or will I even have a shot at all because the tickets were issued by Delta in the first place?

IMO it does not matter who issues the ticket, I got upgrades on AF with a DL ticket. Most airlines will upgrade their own pax first. I would go with whatever gives the best mileage, unless there are guaranteed upgrades x-days out ala CO/NW.