THe first thing I'd try is just disconnect the PAS to see if it then defaults to throttle, or if it just errors out. (I expect the latter, but hope for the former).
If this doesn't work, then:
What assist levels does it have? A number of controllers preinstalled on OEM bikes I've seen have a throttle-only mode, often level 0 of the assist, but sometimes it's the highest level.
If this doesn't work, then:
What happens if you disconnect the display entirely, and just jumper from the battery positive wire on the controller connector for the display to the "KSI" wire (keyswitch / ignition)? I don't know which pin is which on that specific controller, but if it's a standard bafang pinout it should be like the one on the left in this image:
https://manual.eggrider.com/assets/images/cables/eggrider_v2_display_pinout.png
so the Power Lock pin 5 and Battery positive pin 3 are what you need to connect to turn the controller on without the display attached. Some controllers use a different pinout, and if so you can damage things by hooking them up the way teh Bafang uses.
To test which of at least teh two shown above it would be, you'd take the battery off the bike, then use a multimeter set to continuity or the lowest ohms setting. Black meter lead on the bike's battery cradle connector positive pin, red meter lead to each pin on the controller connector until it reads it's lowest reading, or beeps. Note which pin that is. Now move black meter lead to the cradle negative pin, and do the red meter lead on each pin of controller connector again, same process. Now you know which pins are battery and ground, you just need to find out which are data, and the remaining pin is the KSI / power lock pin. That's tougher.
With a multimeter, to test which are data lines, you'd need access to the controller's insides (or the wires inside the cable / connector to the display), while having the display plugged into the controller, *and* the system powered on, so that you can use the voltmeter to measure the wires to see which ones have around 2.5v on them--those are the data lines. However, if you already have it opened up, you can directly measure voltages on *all* the wires to this connector, and then you simply need to connect the two that both have battery voltage on them when the system is powered on from the display. Doing measuring with the power on and things disassembled has risks (zapping you, frying ebike parts, etc), however.
If the pads the wires are soldered to on the controller board (or display board if you open the display instead) are marked in a recognizable "plain" way, this may tell you which are which without doing any measuring with or without power on. (taking things apart also has risks of damaging parts...but it's less risk than doing it with power on
).
I suspect that it's not saving the setting at power off because it's specifically designed not to save any setting that makes it operate differently than the OEM factory defaults. That may not be the case, but it certainly makes things easier for support personnel--they just tell you to turn it off and back on and then it "magically" works like it did before, if the problem was a user-altered setting (which is a fairly common problem and fix for quite a lot of technology).
I doubt that changing the display would make a difference, but it is possible that for this system the settings are stored in it rather than the controller. It's more likely you'd need to change them as a set (displays and controllers aren't widely intercompatible; parts from OEMs may have different firmware on them than even the identical hardware for non-OEM (or different OEMs) versions, so even if they connect up they may not operate as expected).
If you want the pedals to be able to control the speed of the trike as easily as the throttle does you can do what I did on my SB Cruiser trike to do this. The Cycle Analyst v3 from http://ebikes.ca can take the input from the existing PAS sensor (and throttle) and output just a pure throttle signal to any old dumb controller that has the power level you want from the Daymak, based on whatever settings you choose in it (including power and speed limits if you like).
It also can monitor battery info, which is useful for troubleshooting problems when they occur, if you want that feature.
I would recommend the CA-SA version, so it comes with an external shunt for battery current monitoring (and hooking up to power to run it), and it's own separate wheelspeed sensor.
If you get the plain CA version you'd need to wire up a connector on your controller (opening it up, locating solder pads on the board, and soldering wires to them) to use all it's features.
ATM I'm using one generic dumb controller and one Grinfineon, both controlled by the one CAv3 from my PAS cadence sensor (with the throttle also connected to it for times I can't pedal or at least not hard enough to get started). Each controller runs one of the rear wheel hubmotors.