I see Suart's point about most pressure drop occurring across the control valve, at least in vapor-phase operation (otherwise, the control valve wouldn't offer any control). But a slightly opened valve, that would give a small mass flow of vapor, would correspond to a high mass flow of liquid.
Test of that: Jim, could you regulate the flame with the control valve (on the fuel bottle?) during liquid-feed operation? Versus if the orifice functioned as an expansion valve, it would define a set mass-flow of propane.
My trouble with assuming vaporization in the tubing is that it there is so little surface area to absorb the BTUs to provide the Heat of Vaporization - I'd expect that small diameter line to get quite cold and noticeable ice up.
Jim: I wouldn't fret about bursting pressures in a small diameter line. I'll teach you that calc someday, but small diameter lines are inherently high-pressure rated. You can't make them thin enough or you'd puncture, bend them, and any minimal tubing thickness provides huge burst strength. Especially compared to that thin-walled Benzomatic canister of MUCH great diameter.
And remember, the pressure is greatest in the tank, then in the tubing, and lowest right at the orifice. Otherwise, flow wouldn't happen.
And, for completeness: Could there be some crazy pick-up tube inside the Benzomatic canister? The reverse of a chainsaw fuel pick-up tube? You can operate a chainsaw sideways and upside down because the fuel pick-up is a flexible tube with a weight on it. So when the fuel falls to a different side of the fuel tank, the end of the pick-up tube falls with it and settles at the lowest point within the liquid fuel. You could make a tank with a tube with a float so it was vapor-feed in any position. Seems like a bother, but it would allow you to operate in any position and that would add a lot of safety for some applications. Any rattling if you shake the Benzomatic can?
(Sorry, I know you want to save those 100% propane canisters, but) the clearest test might be to run it for a while in "liquid-feed" mode and check tank temp before and after. If it is truly liquid-feed, there won't be any temp drop. If it is phase-feed - if it is vaporizing in the tank - the temp temp will drop noticeable over time. My non-contact IR thermometer would be handy for detecting that temp drop quickly. Image the bottom of the tank where the liquid feed is, it will get the coldest. But you knew that.
Editted to add: Oops, I couldn't see the photos while composing that. The valve is on the STOVE, not the tank. And you couldn't get flare-up on 100% propane but you could on a butane mix? Hmmmm. I'm liking the idea of a floating pick-up tube more - give it a shake and listen. And/or cut one open once exhausted.
I need to get me some of those Benzomatic canisters. For all sorts of reasons.