You have come to the right place! :)
Interesting problem. The pros here will have a clue, but I'm sure it would help to report what year your RV is, whether the furnace has had any maintenance such as cleaning the orifice etc, and the make of the two- bottle regulator.
I was unaware that an LP bottle made a lower pressure than a full one. True?
If the farther bottle has lower pressure than the nearer one, does that affect any other LP appliances? Can the stove, fridge, and water heater run all at once on that farther bottle when it is half full?
The pigtails themselves can have "issues".
As a test, if the near bottle is full so the furnace works ok, when you turn on the stove, fridge, and water heater on LP at the same time, does the furnace quit?
At least you know the furnace works! That is a "good thing" ( after getting my 1991 8531 going again)