unlikely, as you can't "push" current into something, it will only draw what is available. Increasing the voltage will probably brighten the leds, but you may damage something else doing so, so is not a recommended way to go. If you want them bright, you will need to wire them into a standard...
Using an esp32 router or portable router and wled, could result in a very easy and cheap controller setup with the added bonus of wled effects when you aren't running a show. As you won't be running a house load of lights, wifi should be just fine for this situation, also I imagine no music...
I installed fpp on a Pi Zero, just for a laugh to see if it would work for my show, and to no surprise it struggles a little but for a small setup and just a simple couple of sequences with say 5000 pixels max, I imagine it would do quite well.
@AAH may be best to advise here as well. I would perhaps send him a private message, or use his contact-us link on his website if you can not get hold of him here, he makes the boards so will be best to advise further.
There may have been a short on the board which took out the reverse polarity...
That sounds like the diode is shorted so it's conducting in both directions. Was your wiring reversed at any stage? The diode should not fail under normal use.
What do you mean by correct voltage both sides? Test with the power off on the meters diode setting, probes one way should read 0.6 approx and the other way should be open circuit, if it's 0 both ways, the diode is dead.
Do either of the 2 yellow things beside the power wires (Thermal fuses) get hot when powering the board on? Do you have a multimeter on hand to check those diodes beside them as well? Circled in red
The plug will fit, however it needs to be the correct voltage. You may need to measure the output to your LED string while the string is connected, I suspect you will see something around 26V AC.
I can't suggest anything as I don't use Amazon, and have never had luck finding replacement plugs...
That one appears to be DC output according to it's specs. Unlikely to work but they may very well be confusing "DC" for the "AC" that it actually does output, as the polarity swaps to light up the LED's as their polarity in the wiring swaps every led to to give the "twinkle" or "chase" type effect.