G'Day
You are correct there are as of yet no H or N "super" reps of 003 or 113. Though they are not that popular these days , I think the dealers still stock the 113.
Do you know what the "issues are?
If you dont know what the "tells" Are I wouldn't investigate any further and spoil your interest in the watch and just enjoy the watches for what they are , faults and all.
The other option is Davidsen/DSN he might have some 003's and with their closed caseback and better lume , they could be a better bet than the 113.
Lastly DSN white dialled Slytec. the reference 5218-207a . These are rare as , in the really world. But might be the most accurately white faced current rep.
Or there is always 188 chrono
As a noob I would wait a bit before pursuing the very costly franken option
Here is my Whitey