I was able to access the FCL on similar schedules before my flight started by showing them just the F BP ZRH-XXX (direct turnaround elsewhere to start the F trip)

As long as OP can do OLCI, it should work, if Swiss hasn't "enhanced" their systems. If OLCI doesn't work, OP will be in trouble anyway, as his turnaround time in BEG will be too short to obtain a boarding pass before the flight will close.

So, in that case, if OLCI fails, OP NEEDS to try the checkin machines in ZRH, and if they fail too, "beg" the staff at a checkin counter to check him in for BEG-ZRH-XXX.

BEG should be fine with OLCI, but it's about 5 years since I flew from there, and depending on the final destination that OP will fly, you never know..