Yes I do both those things, I wrap a pillow case around the bird to hold the wings and initially grab it by the feet and gently turn it up side down. No fuss.
I was even told that the bird will even stick its head up in the right place for the 'broomstick' to look around - this is also true and helpful.
Usually though, the head is presented to one side rather than fully face down. This was one of the details I needed to know because i was thinking of cutting a shape into the base(pallet) to help it to be face down if that helped the procedure.
Also been also been told NOT to restrict the wings because this is a vital part of getting blood moving in its final seconds.
Also, when the head is trapped I want to pull the neck from near the body not from the feet - but thats where the number of hands i have run out.
I got a bit spooked with the last one I did because it flapped for much longer than the others and I eventually pulled the head right off in my effort to be absolutely sure.
I hatch my own so I will always have cockerele but my worse case scenario is causing unnecessary suffering.