I don't have any experience with bladder surgery. We went the dissolving route with Beandip. The short answer is that it worked very well for us. However, we didn't have everything dissolved/passed on our first try. He suffered for a year with on and off problems before I got him on different food and some medicine to dissolve the crystals/stones, and to keep them from coming back.
However, I don't think Beandip ever had enough of a "mass" in there to show up on an xray. His xrays were always clear. He just kept producing crystals and passing them. He was only blocked once. It sounds like Jasper does have more going on in there, so that could be a different story.
I think the temporary 'dissolving' food is a good idea either way, for now. When you came back with the news, I was thinking he might need some "stronger" food...why I asked.
Let us know what the vet says.