If it were me, I would go for the 2 hour connection. Or if time is not important, the 20 hour connection and leave the airport. There are hotels available through Discover Qatar for c.US$20.

8 hours overnight might not be all that relaxing midway through a long journey like yours, but others may disagree. If a lounge is important and you have any oneworld status, you will be able to use one of the status lounges on an upgraded ticket, or pay to enter a lounge (which will likely be much less than than the fare upgrade).

Also bear in mind that if you do buy the J ticket, the very cheapest P bucket fares do not include access to Al Mourjan.