Here's how I'd approach this:

I see four issues:

1. female connector end-pin is browning (impending doom in the next X years for that one wire's connection)
2. missing male connector -- 11 wires hard-soldered to board
3. male connector pin on other board -- may be an issue (at least clean them up good)
4. future trouble-shooting is impaired if you want to hot swap boards (X days/years down the line)

I would be considering:

A. Am I likely to sell?
B. Do I have other boards to hot-swap this board if there's an issue, or am I just buying a new board if this one dies?
C. How well can I deal with securing pads and ensuring all new pins have good contact in a fix?
D. Does fixing 1 impact fixing 2 in any way? In terms of time or parts or ease of fix? Or can I consider them separate fixes?
E. Is there any reason to think the "hacky" board work is impacting heat in the system?
F. Is the system stable right now? (you said yes).

Conclusions:
I. Fix the connector. It will make you feel REALLY good. Takes about an hour. Time well spent.
II. Inspect and clean up the male pin well on the other board, and consider swapping those pins out as well based on inspection.
III. I'd initially lean toward "if it ain't broke" on the missing male connector. HOWEVER, based on my A, B, C, D and E answers, I may choose to repair it as well. For example, I typically have a couple games in the same release bucket (system 6, system 7, etc) and so hot-swapping boards is a luxury I intentionally set up in my collection to help isolate problems.

Ha, my hour estimate -- I meant for the female housing re-pin...

-mof