Hi! No SR Trains out of Central offer FC, I'm afraid.
So let's pop to GQS. The station is a fifteen-minute walk away, and there's a wee free bus you can use as well. (The 398 is free to rail users and links the 2 stations and the bus station). I'm assuming you have reservations which means you must take the 1646 down? If so...
1341 QS-Perth (you would have enough time to go by train, changing at Partck for this one, or perhaps changing at Anniesland onto a direct high-level service) and a return service would be good. It's a nice scenic line and the fast (Aberdeen) services offer FC, I presume other will as well. The return service gets you in with half an hour to do the Cross-City connection, but there are probably more stopping options leaving you with extra time.
If you want to return to KX London, I'd recommend taking the 1341 to Dundee (a1500) or Arbroath (a1518) and go SB on the NXEC HST (dDundee 1603 or Arbroath 1545) which would take you directly into London, and you get some fantastic rolling stock!
The other (more obvious) option is to bash the local lines. Paisley's quite a good line, so you can go on to Ayr, Ardrossan, Largs, Wemyss Bay or Gourock and return quite easilty within the 3 hours you have. Haven't had the oppertunity to do them all myself, but they are said to be quite good lines. Unfortunately, they offer no FC service. (Unfortunately, I don't think Largs is viable as the arrival time of your train means you've probably missed it and would have to wait an hour...)
I'd avoid Helensburgh at all costs! 320s are not what you want to do!
There are probably other options, but if you particularly want/have to use another SB Pendo, stick to the Ayrshire/Inverclyde lines. If you don't mind going to KX, there are plenty of options!
Also, I'm assuming it's a weekday trip? If you can confirm this, it makes everything a bit easier!
Enjoy the city while you're up here; its a nice wee place on the one day a year we get sun