Looks to me like you've diagnosed your own problem!

The auxiliary pump you refer to is more commonly referred to as a charge pump. It's job as you are probably already aware is to supply pilot pressure to any valves in the system, release the brakes and maybe most importantly keep the closed loop drive circuit topped up with oil pressure. You get leakage in even the best motors and pumps. The charge pump will keep the oil pressure "charged or topped up" hence the name charge pump I guess? It is a gear driven pump internal to the main piston pump, not one of those mounted on the rear. They are for vibrate and steering. I'd say when it gets warm the charge pump isn't keeping up with internal leaks? Hence the low side pressure dropping. The main piston pump is running out of oil to supply the motors... The charge pump is only small and just spec'd right for the job so the first component to show signs of wear. Make this pump too big and you generate unnecessary heat in the hydraulics and lack of efficiency because it is constantly regulating excess flow back to the tank. The designers want maximum performance and efficiency so the pump is spec'd just enough and not a lot of scope for wear....
Worth checking the charge pump they are easy to get at once pump removed. Not sure if you can get to the pilot pressure regulating valve on that model externally, that I suppose could be dumping oil pressure when warm or enough to cause a problem? But generally they are either open or shut, so I think your pressures would be low even when cold? But an easy thing to check before diving too deep.