Chris, I had that problem many times with the old sport rims. Give the middle area a good clean and paint the weld areas with a couple coats of contact cement. Learned that from a tire jockey. In addition to being glue, air pressure and centrifugal force will keep it against the rim and into the microcracks. At the next tire change it was all still fine, just aged brown. I also did the base of the valve stem. Cheap easy fix, best done at a tire change.

I also find the tire shops mostly do a minimal cleaning of the bead area, another area for slow leaks. I usually take them home for a proper cleaning (softer fine brass wire wheel) and bring them back the next day for mounting and balancing. I'll even sand and repaint the lip if it's really bad or any hint of bare metal.

BTW I'm now a big fan of paying extra for a dynamic load balance. More and more shops now have these expensive machines. Those machines tell you when it can't be balanced within spec, whether it's the rim or the tire. If it's the tire, get a note on the receipt that you can use for warranty replacement. Done that twice now and these were decent brand tires. There was a small vibration at only certain high speeds on only certain road surfaces. Moving the wheels back/front proved it was the wheels, brand new at the time. The original tire shop rechecked and said they were properly balanced.
--
Dave -still with 940's, prev 740/240/140/120 You'd think I'd have learned by now