Can you do a trial ride and determine if you have "enough" low gear for the hills?
Also, do you "spin out" on the down hills?
12-28 = 12-14-16-18-21-24-28
11-28 = 11-13-15-18-21-24-28
Going to an 11T top cog will only help on the down hill, IF you are spinning out on the 12T.
However, it's going to make a bigger "gap" on 4th to 5th gears! (3 vs 2 tooth jump)
That's a pretty
BIG gap! I know I would hate it.
Your 4 lower gears are the SAME.
Obviously, a 4T "gap" in the bottom gears is fine. You wouldn't consider it in the upper 2 gears, if you get my drift.
There is another option that you "might" explore-
I had the same 12-28 as you.
I bought a 13-26 (13-15-17-19-21-23-26)
I "combined" them to make a 13-14-15-16-17-19-23, for my flat land MB "commuter" type riding.
You might be able to do something similar to "tune" your cassette for various rides.
You pretty much have to make sure your low gear is "low enough:, which doesn't leave a lot of options for the higher gears.
Now if your shifters have a "friction mode", you could upgrade the number of speeds without the major expense of new shifters. Just a new FH Body, cassette & chain.
EDIT:
That was a good catch by Jive Turkey! The 11T requires a Compact FH body. Your bike might have one, but I kind of doubt it.
Go Bulldogs