If you look at the OEM version (and go for the P-option) it looks like you can simply switch Start/Stop by connecting/disconnecting power. That's the one I think I would go for.
The standard model would need someone to press the On and Off buttons. But you would need to be careful, as Playback mode uses those same methods (
eg, holding down the On button for more than a second).
Then you would have to figure out a way of downloading that data remotely!
Meanwhile, I'm wondering about the capabilities of folk at the Tosca end, and whether they would enjoy becoming involved in data capture themselves.
It sure sounds like fun to me!

PS: we talked about RS-232
before!
PPS: I've just noticed a V3.5 on eBay for the "Buy It Now" price of £ 180.