Yes - there are case vents for both the transfer case and the transmission case that usually rise to the firewall like mine did. I don't remember them being tee'd into each other - but could be.
Actually if you've got a 4wd, you'll likely have four such vents for the two differentials and the transfer case and the transmission.
Servicing the transmission by dropping the pan and changing the filter and the gasket -
if done on regular intervals - is more than sufficient and qualifies as a good enough service to the transmission. It also affords you the opportunity to see any debris and junk in the pan - if indeed, there is anything in it.
Yes - the transfer case and the transmission use the same fluid - ATF - and I've just taken the inter seal out the the two so the fluid can move back and forth. Doing that - the transfer case will be significantly overfilled - which is OK with me as I have straight cut gears in mine. The fluid doesn't move around fast enough to cause any starvation.
For the record - there is very little fluid pressure in the cooler lines - just enough to move the fluid through the heat exchanger* (fluid cooler) - and I have seen some tests that indicate about 3-5 lbs/pressure is normal and as you can see, it's very small and quite insignificant.
* this is NOT a "fluid cooler" although some uninformed persons will call it that - it will raise the transmission fluid level to 195F - and that's because the thermostat in the cooling system keeps the engine at that temperature for good reason.
ATF works best at that temperature too - so the idea is to keep the ATF in that range as best as can be done with short hops and long hauls at either end of the driving spectrum.
It's staying at a regular and designed-value temperature that makes a transmission live a good long time. Cold and overheat kills them!
You should not have any restrictions in the steel lines themselves as they are decently large enough to not plug up.
However - the heat exchanger is capable of getting stuffed up from entrained clutch debris and steel/aluminum shards from just about anywhere and it could create enough backpressure to make a rise in pressure in the discharge side of the fluid lines. Rare - but possible. Still, it's unlikely.
MAYBE this transmission was a rebuild exchange and the cooler was never properly changed or flushed (not always a great idea!) and they didn't want to pay for that repair/service and now their failure to do what's right is catching you by your narglies.
So - the steel lines aren't a likely culprit - but the rubber flex hoses are a larger possibility.
I'm gonna guess here and say that when you moved the cooler line it may have been deteriorated enough to have caused a kink in the line and that could be your problem.
As for the slipping in reverse - it's never good and it can only happen for a few seconds while the clutches burn and they are toast. Boosting pressure may or may not work, and any repair valve to help with a slipping reverse is just a band-aid at best: Your unit needs an internal repair and there are no mechanic-in-a-can that will likely work much - or at all.
OK - here's another part to check - ARE THESE REALLY cooler flex hoses or someone's mistake when they put vacuum hose or garden hose on the lines for a cheap and incorrect repair?
Hey! - late epiphany! - check to see if someone put rubber hose in the fluid lines
near the transmission itself.
There could be a ruptured hose of questionable quality, or just plain wrong hoses there by ignorance. Or cheapness.
I've seen do-it-yerselfers cut the steel lines because they don't have the right tools (flare nut crowfeet) to access the fittings and just put a piece of rubber hose over the rough ends of where they cut the lines with a pair of sidecutters.
Yup, seen it. Fixed it a few times!