Having seen your other posts on P-shop and Tbrix, I feel obliged to try and help out.
If you want to see a bigger diff in a 700, you can look at Kenny Howard's car (Linuxman51 on Tbrix). He's in the process of fitting an 8.8 from an Explorer into his drag car. You can also search for Dug Strickler's car on Tbrix as well, the Volvette. I seem to recall it's got a 9" in there.
In both cases, I believe shortening and custom axles are needed. I could be wrong: I seem to recall that the diff sits offset to the passenger side a little, so maybe only shortening the driver's side so that it can use a passenger side axle is all that's needed.
Since you swapped axles when switching to the 3.73 gears I gave you, you are familiar with the issues involved in putting a bigger axle back there: The torque rods bolt to the side of the diff, and when putting a bigger diff in there it also stands to reason that the torque rods will be moved outboard. This might cause problems in the 700. You've also got to keep in mind the tube diameter because the trailing arm bushings ride directly on the axle tubes.
On P-shop you said that one possibility is the 7.5" out of a SuperCoupe? I don't know if it's got a 7.5" or an 8.8": I thought it had the bigger of the two. What I do know is that the SuperCoupe has IRS. Another possibility was the Lincoln Town Car 8.8, which is 3-4" wider than a 240 rear axle, but much closer to a 740 rear axle. It's still got the wrong bolt pattern, just like the Explorer axle, so you'll have to switch that or run rear wheels that have a 5x4.5" bolt pattern.
You'd probably find it much easier & cheaper to install one of these:
http://www.rocky-road.com/lockright.html $245 and it gets rid of the spider & side gears completely.
Edit - AFAIK, there's no such thing as a Dana 31. It's a Dana 30.
I won't even mention how long a Volvo diff will last behind MUCH more powerful motors than yours by being a bit more considerate towards them. I know that kind of sensible talk will bounce right off you.