The fluid pressure you're reading on the cooler line is "Lube Pressure". In my '67 Chrysler service manual, for example, it lists Lube Pressure in the schematics for the different gear selections as 5-30psi. "Line Pressure" is taken from a fitting on the right side of the transmission after removing a plug and attaching a pressure gauge (the 1957 version might be slightly different than the later aluminum case version, but still similar). Line pressure varies with the gear and mode of operation to well over 200psi in "R".
Removing the accumulator spring is a "standard" hot rod trick to get a little faster apply pressure in the particular circuit. Even the factory shift kits that Mopar Performance sells has that in the changes to make. Grinding the governor weights a little will give higher shift points in all gears and is another "time honored" thing to do in the absence of a factory high-performance governor unit--but going too far can up the shift points too much.
In the case of a line pressure adjustment just because you're towing a trailer, I would think that with no significant power increase, it might not be necessary unless it's a "band aid" fix for an aging trans that might need to be rebuilt anyway. For example, in many of the aftermarket hop up kits for the Dodge Cummins Diesel pickups, where massive power increases take place, they do recommend upping the Line Pressure due to the added power from the engine. Going the other way around with hauling more weight might not make it that necessary, it would seem to me.
Seems like I recall reading that many of the earlier TorqueFlites, even up to about 1965 or so in the aluminum case versions, that "Reverse" could have problems with not engaging all of the time. I'm not sure what the fix was, but it seems it was a valve body issue (maybe a shuttle valve spring?) of some sort. As mentioned, the linkage cable would need to be accurately relaying the "R" pushbutton command to the trans also.
In some cases, when automatic transmissions are stored, moisture from temperature changes in the storage area can cause valve body problems. The trans might be a good, working trans when it's pulled and placed on the floor, for example, but when it's reinstalled a few years later, it might have gear selection problems due to the deterioration/degradation of the valve body mating surfaces. In the case of a friend of mine with a GM Turbo 400, it worked when he got it rebuilt but when he installed it a year or so later, everytime it would shift into high gear, there was some bleedthru that also applied reverse with the same fluid pressure--instant trans brake. As he found out, such situations are somewhat common with used transmissions.
If shift firmness due to the heavier-duty activity is a perceived issue, then probably some different clutch plates and bands for the trans might be in order. Some that have a more agressive friction characteristics, for example, rather than the "smooth shift" factory style items. Not using "wavy" steel plates in the clutch packs will also result in slightly firmer and quicker shifts. The wavy steels were used in 1966 and later trans and if you know what you're feeling, there is a difference in the 1965 and 1966 TFlites--not sure if that's an issue with the earlier cast iron versions, though.
As for raising shift points, that can also be accomplished to a certain degree with the preload adjustment on the kickdown linkage. When we got our 1966 Chrysler, the shift points felt ok in normal driving, but I noted that if more throttle was used, the part throttle shift points seemed to lag until you put enough throttle to get a WOT kickdown situation. This was before the part-throttle kickdown came into play in the early 1970s.
What I found out was that if I shifted the trans manually on normal acceleration and delayed the shift points to a slightly higher speed, especially the 2-3 shift, I could accelerate faster with less throttle. I consulted with the service manager at the local Chrysler dealership and he mentioned that he put more preload into the linkage on his car to do just that for mountain driving. I filed that back for future reference.
When I took the car off to college, the traffic patterns in Lubbock moved faster than down here in the DFW area. Suddenly, I was one of the slow cars in the pack. Doing the manual upshift situation pretty much remedied that. In the case of the 1966 trans, the factory adjustment is 2 turns of preload on the kickdown linkage from hot, base idle. What I did was experiment and make the total 4 turns of preload instead of 2. That upped the part throttle and minimum throttle shift points so that I didn't have to manually shift any more. The car felt better as it took less throttle to do things in normal driving and was more fun to drive.
I also learned to do a version of the part-throttle kickdown manually too, basically emulating what the newer models did. Same result, less throttle and better acceleration without getting into the power mixture of the carb.
When we got the 1972 Chrysler, at the 3000 Mile Check-up, the mechanic tweaked the kickdown adjustment until it felt better and did not lug the motor quite so much at lower speeds. My shadetree guide is to have the car hit 3rd gear on light throttle at about 30mph (depending on the axle ratio, of course) so that rpm did not drop below 1000 rpm when that shift was completed.
When I got my 1980 Chrysler, it was also the victim of a too soon upshift (probably for the CAFE driving cycle). As the adjustment slot for the kickdown linkage was now under the car, I got two black cable ties and put them at the back end of the slot on the kickdown linkage at the carb. Worked fine. I've noticed that same "problem" with other Chrysler vehicles of the 1980s era too.
Many publications mention that you should not mess with the linkage adjustment from factory specs, but I've determined that a little tweaking does not really hurt anything. Basically, it's telling the trans that it has more throttle input that it reallly does, so it delays the upshifts as it "thinks" the driver needs more power and performance. Not lugging the engine on those early upshifts can also result in less heat being put into the trans fluid by the torque converter being in more of a torque multiplication mode. Just another little tweak that discretion must be used with so as to not get things out of whack.
In the case of the 55psi Lube Pressure, that seems a little high compared to the later models. Unless there are some high pressure rubber hose sections in that cooler line, the existing hose integrity could be compromised over a period of time. A failure in that area would not be something to desire, I suspect. You might desire to get a Chrysler factory service manual for that year vehicle to make sure that all fluid pressures are in spec. I also know that many trans shop techs have their own "secret fixes" for various upgrades too, which I respect, but I still might question sometimes.
Another "hot rod" trick for a firmer and quicker shift is to use the Type F trans fluid instead of Dexron variations or the earlier Type A. The "Ford Fluid" has a more agressive initial friction characteristic so the clutch pack/band engagement is firmer and quicker with less initial slippage. This was a somewhat common thing to do in the later 1960s and 1970s for both Chrylser and GM automatics.
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