Instead of flipping the bike over, put it in a stand or hang it by its seat from a rope. I've been using a rope with a bowline loop tied in it as a bike stand for many years. Tie a second rope around the stem if I need the bike steadier. (See any book on sailing knots for instructions on how to tie a bowline. One of the most useful knots there is.)

One advantage of hanging the bike instead of flipping it is that it puts the brake calipers at eye height. A real benefit for wheel truing work.

Ben