It might be a good idea to foam fill both tires on the same axle....and yes, properly foam filling the tires WILL be the solution.
Had my BX tires foam filled over a decade ago (maybe 15 years ago). Happy camper.
I am. Just had the flat off the tractor in the truck. First time I was looking for a business that did this met a dead end. Was 'pumped' when I ran into this tire dealer that was ready to help.