Need Help With Hydro, Climbing Hills

Hi, I've just acquired this Craftsman mower which seems to be in very good condition; Kohler engine runs very strong/smooth. However, the mower operates very poorly when climbing even small hills. (Model# 917.258692 | Hydro #310-0650)

Here's what I've tried: Cleaned hydro exterior, opened up the breather plug on top and used a suction pump to drain all old oil. Replaced with conventional 20W-50 and followed the purge procedure in the owner's manual. Mower began working much better, more responsive, but still struggles on minor slopes.

Questions: Is there a specific type of oil I should be using in the hydro? Is there a way to tighten the drive belt on this model; where's the adjustment point? What else would you check? Thank You!