This is a wonderful idea.

To fight grieving, it could be that the request stays up for 12 or 24 hours, and, when you choose the leve, you have 30 minutes to complete it. If you don't complete it in 30 minutes you can't accept a new one for an hour, if you fail to complete 4 in a row (or something like that) you can't accept a new one for 12 or 24 hours.

However, if you simply fail the attempt, there is no penalty.

The only other problem I could see is the location where the leve shows up. If a request is in a specific town, is it only visible in that town? It would make sense to be that way, but at the same time, it would perpetuate the Ul'dah effect.