1. Does that efficiency increase come at the cost of bandwidth?

Not sure...Never tested that...But it wouldn't suprise me if it did a
little..

2. Does having the load closer to the base increase the band width, if

all other numbers (coil diameter, coil length, etc) are the same?

Ditto....Not sure....But again, probably a bit...
3. Would getting the loading coil above the "steel" increase my
chances
of making a usable antenna with the bandwidth and efficiency I desire?


Yes, as far as efficiency.

Also using a hat would help a lot, although I know you may not be able
to.
But if you could design a hat, that would help current distribution a
lot.
Take a few turns off the coil too...But the more linear current
distribution
is the main benefit, I think more than any decrease in coil losses....
MK