From what I've seen with solenoid valves, you have to go a size up or two to decrease the resistance from the valve. An alternative would be to use a fast acting servo-ball valve. It will be more expensive, but they should make those with the same ID as the pipe you are using so losses are minimal. If you want to use a solenoid, you can use some bell reducers and go up to a half inch solenoid, then reduce back down to 1/4 inch. I think that Parker probably makes all of this stuff if you cant find something by ASCO.

Before you do any of this, I'd recommend getting a ball valve with 1/4" opening and trying to operate it by hand. Those valves are fairly cheap and you could even return it after your test. I have a feeling that your 1/4" tubing may be the restriction with the amount of flow you have going through that thing. You may have to go up to 1/2" to get it to work with propane. Just try it with the hand ball valve and that will confirm if it is just the valve that is restricting the flow so much that you need those high pressures.

compressed air actuated ball valves work excellently. I played around with a few of these at the box shop last year, I was helping a little with a methanol effect with coloring salts, so any diaphram based valve was out, as the salts could shred the valving. The one we used required 110 v in for the air solenoid, compressed air for the piston, and the compressed air and solenoid actuated the ball valve, which was spring returned, so it always defaults to off. Clever piece.

Those actuated ball valves are quick, powerful, and when on, they are just a straight pipe. Might be worth calling Triangle in San Jose and seeing if they have any laying around.