Does your base model motor have the mounting holes for the intermediate shaft support bearing?
I know an F35 can be replaced with an F23 on an LSJ because I've done it. Base model axles and trans mounts, F23 slave cylinder/TOB, and LSJ clutch. I'd imagine the reverse could be done if you can get the intermediate shaft mount attached to the block.
The inner CV splines are different between F23 and F35, the outer CV splines are the same for all Cobalts except for the LNF.
I'm not aware of any F35 with a sensor on the intermediate shaft. Both my F23 and F35 had the speed sensor in the same general location on the transmissions, but the reverse switch is in a different spot on the transmission. You'll need a tune to keep the speedometer accurate, but the speed sensors are otherwise compatible.
If I were in your shoes and I had a non-LSD F35, I'd keep the F23 if it worked fine.
Let me know if you have any more questions or if I haven't answered the ones you've already asked!