The play on the monolever could be because the bearing has been turning on the "adjusting " pin and has worn it.
Motoren Israel has slightly oversize pins which get a better grip of the bearing, and they are cheaper than OEM from Motobins too.
OEM pins are a loose fit in the bearing so if you are going to reinforce the frame it makes sense to tighten up the bearing fit too.
The frame tubes look and work like mild steel to me, you shouldn't really need much better.
My old man used to make a few pannier frames, and he used a thick wall pressure pipe, which was a bit better alloy then stock mild steel and worked/ bent easily too. But that was 50 years ago.
The stuff they currently use for petrol lines in servos is similar and is good gear too, but I dont know if it comes small enough for you.
Adelaide Hills, Australia. 93 R100 GS, 77 R75/7 ,70 BSA B44VS, , 86 R80 G/S PD, 95 BMW Funduro F650 ST