You are correct that the 2 systems are connected, but working with the inching system shouldn't affect the brake side if everything is working/adjusted properly.

You say you've rebuilt the both master cyl's- perhaps the maladjustment occured at that point. The brake system is exactly the same as any light duty truck/car without anti-lock brakes.If you do research on automotive brake systems, it'll get you in the ballpark with your lift

As far as the inching system- it's also very simple in theory & operation. As you depress the inching pedal- 2 distinct operations are in play. 1rst- pressure from the master cylinder applies to a valve in the trans which dumps the pressure which was going to the clutch plates. 2nd- pressure from the master cylinder applies to a piston ( the long cylinder with all the brake lines going to it behind the upright, on the front of the diff)- this cylinder in turn applies pressure to the brakes.

There is a difference in the master cyl's which is important- the brake master cyl ( right side) has a pressure releif valve which holds pressure in the brake system at about 6 lbs. This is to keep all wheel cyl's slightly pressurized to eliminate air seepage into the system. The inching master cyl (left side) has no such provision- no pressure is held in that system.

If the clevis is improperly adjusted (no freeplay) on the brake side, the brakes will slowly but surely hold more & more residual pressure until the brakes become locked. If the clevis on the inching side has no freeplay, the system will also hold more & more resicual pressure, eventually causing the trans to slip.

Also- on this model lift- the parking brake is not in the wheels, but has it's own drum & brake shoes under the trans. Adjust the p.brake to hold the lift still while idling (or just slightly higher than idle). Any looser than that is useless, tighter than that will stretch the cable &/or wear/break the handle assy.