Do not use the stabiliser, the correct senders have built in regulators.
As the temp gage does not move to C when power is applied, but does when grounded, then you are right that the sender is either bad or the wrong one. You will have to get one from any 1955 U.S. Ford product. It has not been available from the aftermarket oem suppliers for many years but some restoration suppliers, T Bird, Crown Victoria etc, have had some reproductions made. I lost faith in this supply line when early ones failed prematurely. I am told that the quality has improved but I prefer to use used ones.
If cleaning the points does not fix the sender, then I think the best solution is for me to send you a pair of used gages and matching senders, unless you know of a place over there that is parting out old American tin.
PM me a mailing address if you choose to go that route.
I assume that the use of an underdash accessory gage set is not something that you want to employ?