I have recently restored a very bad 1947 United Singapore which is very similar to yours.

It had a lot of problems, something which may be in common with yours is bad Jones plug connections. I cleaned them out best I could, used scotchbrite on the male side and put a light coat of oil on them and worked them in/out of each other a zillion times.
I also had to reduce the size of the female side for each pin >> by a small amount<< by means of a long nose pliers to tighten the connection before it became reliable. I inserted a proper size drill bit into the female side that was a bit smaller than the jones plug male end so not to crush the female side with the pliers.

I also could not find a schematic for my United so I reverse engineered my Singapore. It took tens of hours to complete plus the artwork and I am selling them here: https://pinside.com/pinball/forum/topic/for-sale-1947-united-singapore-pinball-schematic-and-diagrams

You probably already know your game originally came with a floor cabinet instead of legs. I assume the steel legs are to replace the floor cabinet.

You may find that a set of hardwood legs may provide a less rigid, spindly support for the game. Nudging is a major part of playing these early EM pins and I am not sure if steel would provide the same effect.

Just a suggestion. Really nice pin, BTW

Hi ramegoom.
The replay counter was probably removed some time ago to comply with law. On my Singapore, With credits on the counter, a coil on the front door would energize when the coin slide began its travel. The energized coil worked an armature to allow the coin slide for free-play.

A small 4 pin Jones plug underneath the pf was to enable or disable free play.

A meter under the pf shows how many games were played that beat the high score, both adjustable score and fixed scores.

Singapore has two under cabinet buttons. One button turns the game off and the other subtracts credits from the unit. Perhaps your mystery button was a subtract credits button.

Me? If it were my game I'd try to install a counter whether it's an original United unit ... Or make a different Mfg unit work. But that's just me being weird.