Have you dealt with Tillotsons much? For some reason, Ryobi line trimmers here from the 1988/89 period, carry them, though one we bought new had a Walbro. Their engines are those American 31cc Ryans supplied to many makers. They have a reed valve and have alot of torque down low, which isn't necessarily ideal for line trimmers, but they also powered optional attachments that require this torque such as leaf blowers, vacs, cultivators(!) and lawn edger attachments via a split boom down the middle of the shaft. They were very big sellers at the time and were available in all department stores and sold like hotcakes. The mower stores, who didn't sell them, would always claim they were junk but I found ours very reliable, if heavy on fuel for a small engine. The Mitsubishi TU 26 powered straight shaft weed walker I currently use is a Prius in comparison and delivers great power for these duties.
I still use an 80s Ryobi with the leaf blower fitting (it's very good) and it has a Tillotson carburettor. It pulls like a train but gets hot after hard use and needs a tea break every now and then lol.