Thanks to all for the suggestions so far. I picked up the Shoe Goo from Ace Hardware along with my new Dremel (only noticing too late it was a dual-speed and not completely variable, but will still work for me for now). Just got done mounting the soles by filling them with paper towels and taping them sole to sole while they set.
I'll do a test fit tomorrow and walk around my living room - hopefully the soles will hold
Oh, and a BTW: I tried a shoe-repair shop years ago with my mesh/leather Sidis. I won't go into the whole sorry affair, but even if my small town had a shoe-repair shop (it doesn't) I wouldn't take that route again. Oh, no - no way!
You don't want to know...
DD