Why not use LT 235/85 R16 ?
here's a tire size calculator:
http://www.1010tires.com/Tools/Tire-Size-Calculator
rim section sidewall
size width width height diameter circum revs/mi
ST 235/80/R16E 6 9.25 7.4 30.8 97.77 654.74
LT 235/85/R16E 6 9.25 7.86 31.73 99.68 635.65
Rating ST 235/80/R16 3420 lbs (E rating)
Rating LT 235/85/R16 3042 lbs (E rating)
Lower rating for LT 235/85/R16E is not an issue for me.
CAT scales with rig fully loaded revealed:
Trailer weight: 9,860 lbs.
Pin weight: 1,880 lbs.
Trailer Axle wt: 7,980 lbs.
4 tires @ 3042 = 12,168 lbs.
Trailer GAWR(each) 10,400 lbs (2 x 5,200)
Tire safety margin: 4,188 lbs. (12,168 - 7,980)
Axle safety margin: 2,420 lbs. (10,400 - 7,980
Tires are rated higher than GAWR
This seems ok for me.
Figure what works for you.
You may be able to use the same rims if weights allow.