John Deere LX255 Differential lock?

[phuz]

This is our second year in our new home and I want to get the snow cleanup situation perfected this year. Last year I bought a Snow-Thrower for the front of the tractor and these things are extremely heavy. I put chains on, and even fabbed up a bracket and 1/2" bar where I could attach barbell weights. With 70lbs hanging off the rear of the tractor, I still only made it half way up the driveway. I found another post where someone had 240lbs added to the back so obviously I need more weight, but my real question is:
Is there any way to lock this differential?

I had looked at welding sprockets to the axles and installing a shaft to keep both wheels in sync, but not enough clearance.

Any other ideas?