That is what old toe straps are for. I fold the tire up into 4ths or 5ths depending on the tire and use a wrap to keep the tire from getting pinched. I use an old dress sock, but it never rains here, there used to be tubular tire bags, an old French cycling newspaper is acceptable too. I nest the tire so it does not interfere with my thighs and tucks in between the saddle rails, it will overhang out the back.

If you go with Vittoria Rallys use the 23 mm examples. I would take a 25 mm tire over a 21 mm any day. There are plenty of tires out there, I always go with natural sidewalls, but that is just me. Back in the "gutta" adhesive days, it was best to have the spare not being new, but mounted and used before, the residual glue did a great job of keeping the spare on the rim after it was mounted on the road. It has been a long time since I have flatted, I just retired a rear tire due to wear. WIth the new adhesive, I am not sure of its "retack" capabilities, maybe rim tape... but I would just mount it and ride carefully on a spare if I had to today.

I do not see much difference between the Contineltal or Vittoria glue manufactured today.

One idea would be pay the bike shop price to buy a new tire if the local shop would let you watch them installing a tire, and mount the tire while barefoot, toes do a great job of keeping the rim where you want as you work the tire on, valve at the top.