Even with the pictures, it's hard to see just how close the supports are to the tire, but...
... as can also be seen in the pictures, it would seem that the shop that sold me the tire and installed same apparently felt they had done me a favor and installed a tire that was taller and wider than the bike is supposed to have on it.
Given that, it would seem that the problem is that Suzuki expected more clearance from the original tires and didn't leave all that much room for wider/taller tires.
In my case, the wider (for those, like me before reading the information and learning along the way) comes from the "90" portion of the tire size. The tire width is 90 percent of the height, which in this case would be the 150 portion of the tire size.
The original tire would have been a 140/80, so it would have been shorter and skinnier (only 80 percent of the 140).
I can order the smaller tire and get it installed, or... well, replace the shocks with the ones that I've ordered via eBay and see how that holds up.
At this point, I'd rather go with the shocks, though I may change my tune when I get the shocks and find them a total p-i-t-a to install

(hopefully not, but I don't want to count my chickens...)