As nice as it would be, I am sure... I'm in two minds about saying GO FOR IT to getting another dog so soon. If you've exhausted all avenues for finding Jack, and are at a conclusion that it's unlikely he's coming home, then maybe, but what if he does happen to show up - could you manage/keep a third dog? Would you keep the newly adopted dog or rehome?
I'd also be careful choosing the same mix or similar breeds to Jack given he was a mix of breeds that are quite capable, agile and intelligent enough to want to escape a yard... and I'd also want to be really comfortable with any dog if they were put up for rescue due to being bored and/or serial escapees. Make sure your fences are all 100% secure and that a new dog won't escape in a similar fashion to Jack.
I also think that while it's great having detailed descriptions on the dogs up for rescue, the only way you can really be sure that a dog is right for you is to meet the dog in person and also go through an experienced rescue who can place dogs very well into new homes, to ensure that the dogs don't have to be returned.

Sorry for being a bit negative here. I'm not intending to offend or upset. Just looking at it from a different POV.