And to answer your question it’s only forward and backwards. Definitely from rear wheels. I had a front axle repaired a year ago and then saw I had a leak from left front tire. Took it off and all the hub bolts were hand tight. Hard to get good work done these days. Tightened them up and just added new oil. No I haven’t gone with a heavier oil. Just use what manufacture recommends. But guess that would be a good start to change out the hydraulic fluid and filter. What oil do you recommend going with? I live in Texas so it’s hotter than a ghost pepper right now.
For the front axle only, the book list 80/90w gear oil or hydralic same ad transmission. The general wisdom is swap front axles to gear oil.
Back to your issue; it could be brakes stuck on. Straight forward or backward would not be diff lock. Any chance something is rubbing?
You don't want to swap hydro un the transmission for gear oil; that's only the front axle.
My Ck2610 is similar machine, But I don't have split peddle brakes; I think one of the higher trim models of CKs did; so if yours has split brakes, make sure both are released.
Edit; I didn't see the other post; about it being the diff lock lever. If it was trying to engage, yeah, that would grind. Mine, you have to actively step on the diff lock lever to engage it, and then spring tension disengages when you lift your left foot up. If your somehow got jammed half way in/out of diff lock;... Try placing the HST (if yours is HST) in neutral, machine off, brakes off, and use the wheel to rock the machine, and see if it still binds. Also, you could jack up the rear (be very careful, as the front axle will pivot) and hand spin the wheels. Getting the wheels off the ground may allow you to easier engage/disengage the diff lock.