Hmmm. I'm trying to think of a way to do this that is going to be better than just buying a new receiver. I'm still coming up to speed on this year's crop of receivers (and some new price points that are out there), but about six months ago you could get the Onkyo 506 for under $200 - and I think that it would beat that Sony hands down. I still have to find my bargain receiver for this year, though. I only mention that as a point of reference for when you're deciding what to do. You don't need to spend a lot of money to get a new receiver these days.
My leading option right now is this - for $20, you can buy a box that will convert speaker-level signals to line-level signals (like
this one from Crutchfield). You could connect the "B" speaker outputs to that box, then connect the RCA line-level outputs from the box to your sub. With that type of connection, you would be able to control the volume of the sub from your receiver. You wouldn't be able to redirect any of the bass from the other speakers to the sub, but the sub would play the same bass that was being sent to the front speakers (and you'd control the frequencies using the crossover dial on the sub, assuming it has one - I'll go check that HK site in a second).
You could also use the REC OUT jacks from the TAPE/MD connections on the receiver (like you mentioned above), but that output is not controlled by the volume control on the receiver. It will be a fairly high signal level, too. So, that is not a good way to go, IMO. You can always try it, but I suggest that you start with the volume knob on the sub turned all of the way down to prevent it from getting damaged from the high signal.