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AFAIK michelin dynamic classic come in 700x20c, and have a bit of puncture protection. Conti supersonics are sometimes cheap to buy second hand - I recently got a pair from kleinanzeigen for 30€, but they have no protection.
can`t say anything about tubeless, no experience in this area.
for the width: I´m not sure if I understand you correctly, you mean the distance from rim hook to hook? "traditional-sized" narrow road rims should be okay, I think the most of them are like 13mm-ish internal.
I have a rear tyre clearance issue that if anyone could advise on would be greatly appreciated.
I bought a boschetti (probably custom 90's tri) frame recently and the tyre clearance to the seat tube is tiny. A 700x23c clincher around 100psi on 15/18mm diameter rims rubs on the seat tube. Due to the move away from skinny tyres, 18c or 20c clinchers are hard to find and most are race orientated so don't have much durability. The clearance to the seat tube is around 22mm at on a 700c wheel without tyre. I have only really used clinchers but wonder if tubeless may have a lower profile tyre as they are run at lower pressures, especially on a wider rim.
The skinny tyre then leads to wheel width questions. The ETRTO recommendations seem to be on the high side. What would people recommend for wheel internal/external diameter for thin tyres as a real world low level limit?