I've fitted my JD LT155's with Carlise Tyres (keeping within the standard 20x10-8' footprint) with great success to improve traction-
Number 1 is running SL (Super Lug & will just about climb mountains ! ), rather too agressive a bar style ag tyre patten for nomal lawn use, but I needed this mower specifically set up for max. stability/traction for mowing on damp clay soil around a undulating pond bank.
Number 2 runs Turf Masters, a commercial grade which seem to balance my traction/lawn demands on reasonably undulating/slippery terrain pretty well
Here's a link to the Carlise site which may assist:-
Carlisle Transportation Products
IMO - the tyre stores generally don't know much about mower tyres & seem to recommend product which they either have in stock or make the most margin on....
I'd also be cautious about upsizing tyres, as a little extra gain in speed will probably be compromised by increased loading on driveline through reduced transmission torque available from start up & reduce transmission life through increased heat/strain (the LT155 Hydro's whilst good in the model are little marginally under constant high heat applications, with life prolonged by regular oil chainging) - A 0.5 increase to 6mph doesn't sound much in theory, but as a minimum it is going to place c.10% demand/wear increase on all components...engine/driveline...etc..which is exponentially increases driveline loading with the reduced tranny torque available from start up.
Good luck & keep the thread updated with the tyres you purchase & how they perform.