I made a tool to do this.
I get a lot of punctures so end up patching about twice a month. I carry 2 spare tube and last-resort stickers, so I patch in the comfort of home not on the side of the road. This tool replaces the valve cap, and as it threads on a small bolt down through the middle is enough to press the schrader's pin.
It started off as a decorative cap that looked like this:
I lopped the end off, drilled a hole vertically on center and then "tapped" it for the small bolt for depressing the pin.
There are two holes through the sides to let air escape. One would have been enough, but two was quieter and less likely to be obscured. Two more might be good.
Originally the bolt was threadded to permit adjusting of the flow rate, but in practice you want the tube empty.
So I fit this then start folding the tube from the opposite side to where the valve is. I layer it into flakes about as wide as my hand and then pinch it around the bend with my fingers. Once at the end I swap the deflator for a normal cap. and then shake the tube out and reroll it with the valve in the middle.
If that's not clear let me know and I'll expand with more photos.
By "thread" I mean ramming a series of sacrificial bolts through a hole until it formed a thread-like shape. The chowdering on the outside is because my main tools were a drill press (pillar drill) and a machine vise.... ideally I'd have used a lathe, and some better way of supporting the cap. An old valve stem could have been a lot better. And I should have put some light chain under the bolt, to provide a handle. This little thing likes to drop and roll under stuff.