So, since having FFS which included a tracheal shave, my falsetto has gotten lower. My throat feels different now. It feels like I am straining to get to falsetto.

Did anyone els experince somehing similar?  Did it go away after a while?  Could I get it back with some work?  After all the swelling goes down (I'm still pretty swollen)?

Any thoughts?

How long ago was the shave?
Swelling can, as anyone who ever had a strep throat knows, make your voice different and even lower until the swelling passes.
The shaving procedure can sometime hurt the vocal folds a bit, if you are less than a month after surgery I'd suggest to wait until at least a month or two passes.

Another thing, ask your surgeon, ask a doctor.

It could be the breathing tube too.  I know my throat was hurting for a few weeks from that thing.  One voice surgeon I consulted with said that he wouldn't do surgery on someone that was going to be undergoing general anesthesia within 6 months after, because of the damaging breathing tube, so I guess that has some potential impact on vocal cords.   But this is temporary, and they heal. Not sure that would be applicable for your condition.

Apparently different surgeons vary in how aggressively they remove the excess thyroid cartilage.

Possibly some use just a scalpel if the patient is very young and the cartilage is soft. (I'm just guessing.)
Many use "rongeurs", hand-held nippers, to chunk away more hardened cartilage.
Some surgeons use a power burr to grind away the cartilage.

I've never seen a discussion of the esthetic benefits versus risk to the voice of varying degrees of aggressiveness of the surgery.

Does anyone have any references to this matter?

During my trach shave, the surgeon took off just a bit too much of the thyroid cartilage. This resulted in a collapse of my vocal cords. I was able to talk, but I lost most of my vocal range. I had to go through some pretty extensive voice therapy to get my voice back to a usable level. I never regained my upper registers. And my singing voice is totally shot.

I consider this a minor complication. Overall, I was very, very happy with the ffs work. And since this was the worst complication of my transition, I feel very fortunate.