Here's a development.
I have found the controller is a guagemaster 100M it gives off 13.89Volts and is rated at 14V output.
What power supply does the Stainz require? As it does run at this voltage.
Voltage is irrelevant (except the Maximum) as the Loco's Speed will be dependant on the Voltage Given to it. You are well within the accepted parameters with that Gaugemaster Setup. I would be looking at no more than Half Speed given, without looking at a Vid of the Setup it is difficult to define what you are doing in terms of Speed. But a good steady Trundle would be best both for the Loco's Life and staying on the Track capability. I would still however suggest an LGB Controller in such a situation, perhaps the 51070. This will give a Maximum output of 24v which is the Maximum for LGB. However at that the speed would be ridiculous, however at a sensible say 1/2 Speed it should be about right and have a Very Long Life as it will be well underated.
With regards to Track, you should be looking at Bog Standard LGB Track, keep it in place with the little track Clips LGB Ref 11500. No tightening of curves or manual bending of straights. These Clips slot into the Sleepers underneath between each joint and will tend to stop the Track Separating. This could be a problem as large gaps in the Rail though sounding good will cause additional wear. I would also recommend LGB 51010 Graphite Paste on each Sleeper Joint. Helps with Voltage Supply.
Some years back I got given a Stainz that had had a very hard life on a similar demo thing in a Shop. The wheels were like yours, valve gear all sloppy and badly worn. But it still ran like a trojan after some gentle oiling of the complete mechanism. You could probably think about that as well, the Turning Monthly could coincide with regular Service a few spots of LGB Varying Lubs as recommended by LGB 51020 Gear Lubricant. And do not forget the LGB Red Lub 50019 on all bearings of Rolling Stock periodically as well. This would include the Bogie Type Turning Mech underneath the Vehicles both Bogie and 4 Wheelers. This stuff will also be the thing for your Stainz Valve Gear and any of the rubbing surfaces on the Chassis.
Hope this helps,
JonD