I would think castors on front would exacerbate the problem.
You are probably already mowing in a "partial skid", with the front of the mower uphill from the rear.
Castors would mean you have only 1/2 the wheels to keep you from sliding down the hill.

I'm not sure how the large wheels would fare with the heavy side thrust?? They are typically found on cheaper mowers that tend to have a premature death on the drive train parts. Smaller wheels wouldn't produce as much strain on the axle bushings.

That big of a lawn deserves a good quality mower for YOUR sake.

I visited a show called Saltex at NEC which specialises in Garden & Landscaping Machinery and Equipment. it was unindated with Castors and Wheels Suppliers. Pneumatic Wheels, Castors, Wheels and other types of products that would be of interested and they are very helpful for my own requirements (which were business related for new equipment design). I went with Bulldog Castors Ltd, but there were many other supplier. More than 10 I guess. The Saltex show runs every year at NEC, give it a try

Bill_k is right - your mower will want to dive and you will be fighting to keep the nose parallel to the bottom of the hill. If u search for a post - try casters, someone explained - u fight the mower because it want to wander everywhere but stationary front wheels will keep u from diving to the bottom of the hill.