Found a interesting custom tool for these type of rivets on eBay, used for Tonka Trucks of all things.
TONKA NYLINT BUDDY L STRUCTO, RIVET TOOL FOR 1/8" SEMITUBULAR RIVETS Fixt DiesI think it will just enough bite to get to the farthest rivet. I sent a ton of photos to the seller (maker I believe) and thinks it will work but if not he will accept a return for a refund. The tool is at the high end of what I want to pay for one but it's much cheaper than "real" rivet tools.
Also, hansonrivet.com is sending me a bunch of sample rivets to try.