How about a new 24-hour one-vs-one match play format?
You challenge someone else, and you both have one 24-hour period to complete a round on the exact same course. You can disconnect as many times as you want, as long as you complete the round before the 24-hour period. If you don't complete a round, you automatically lose (if both players don't complete it, then it's an automatic draw - or loss for both players).
The round is scored the exact same way as a match play game. In other words, if Player One scores better on hole one, then he/she is one-up. If Player One is three-up with two holes to play, then the last two holes don't matter.
This would essentially negate the problem of people dropping out, and people getting unfair wins/losses just because of inherent WGT connection issues.
The only problem is that there would be no 'live' element and a lack of social interaction. But some people don't care about that; they just want the competition.
There could be an option to score it based on strokes too. Or a skins option. This can also be generalized to two-vs-two or three-vs-three (and so forth).