I am a southpaw but pretty ambidextrous
I usually go
Sitting on a short stool or a bucket
Bird feet up - back of the tail on my right thigh
Head basically against my left (outer side of my) chest
Left arm traps both wings against my chest, and I can raise my hand to cover their eyes if they are losing it. Right hand can part feathers and I can send a video of wing clipping if you’d like.
They don’t usually panic when their eyes are covered, so that right wing doesn’t typically prove to be a problem if I need to cover their eyes w my hand.
Holding them on their back like that seems to calm them down quickly.
I know that it also puts a lot of pressure on their lungs (esp for turkeys), so I quickly check them out and/ or clip wings and get them back on their feet.
If I’m just doing a health check and find anything of concern on the belly, near the vent, or under the wings, I can usually put them on the ground between my calves, head facing me, and wings between my calves to check their back without a huge fight to verify what I am looking at. The bucket “seat” works better for that, because they don’t see an escape route - the way they do when looking through the legs of a stool
I won’t likely be able to send pix until tomorrow, but lmk if it would be helpful!