what I do is match the ign key to the petrol/seat locks. if the key goes in then you can modify the plates inside the lock. its fecking fiddley but doable and smallish fingers helps.
I have a B12 swinger in my 750 ET, i just used a sleeve. i found an aluminium tube on the bay of E with a 20mm O.D and a 14mm I.D. cut it to the length i needed and slotted it in. it was a very snug fit which is good so no play what so ever.
has someone welded a brace on your frame at some point ? looking at mine it doesn't have one but i was just thinking its possible to make one that bolts to the front engine mounts.
it must be my dodgy old eyes if its defo straight then it must be the frame lugs, but i wouldn't try to bend them back as it could end up in tears if they snap off.
that footrest hanger is defo bent and needs tweaking straight, if all else fails you could put some washers behind it to pull it away from the swinger.
wern't they restricted through the carbs/ignition ???? not sure with the European bikes. Crooks Suzuki is where i used to work and it Furness by the way.
I can't see the float heights causing the hanging idle ? but yeah it will effect the mixture. ive seen floats set at all different heights and it would idle ok. but its worth a try I suppose