Forget time restrictions.
I'd love to see WGT implement computer linking. Everything on my screen can be seen by WGT. Simply implement the policy "Players who finish high in premium tournaments may be required to play a linked round at the same course under the same conditions."
Extra work for WGT? Not really as i would imagine there would be plenty of volunteers in every time zone happy to oblige.
The cheats? Well, if you can shoot "x" at that course under those conditions in single play, you should be able to play reasonably close to that score whilst linked. Surely. Those that rely on cheats will fall apart very quickly. If they try to use their cheats that'll be spotted at the other end in seconds.
The cheats will get found out soon enough, or will have to make do finishing way down the list. Every honest player will have absolutely zero to worry about.
Those that kick up a storm of protest and all of a sudden can't be active much anymore...well, I think that would be rather dubious. Those that reckon their PC's are "too sensitive with personal info" - no problem - use another computer and until such time your suspended.
I personally would welcome the scrutiny and consider it another part of the fun of WGT. Indeed, an honour.