Just another idea for a laser measurer, if there are any engineers out there.
What about two lasers on each end of a 24" crossbar? The two lasers on the ends would be pointed downward, and determine the distance to the ground. (Lasers are used for measuring distances across a room, etc., but I'm not sure if they would be accurate enough for measuring horses within the 34" range or not though.) The crossbar would be placed on the horse at the measuring point (last hair of the mane). It could have a bulls-eye 'bubble' in the middle and a switch of some kind to activate it when the bar shows level, and a digital readout giving the height. Or, if the technology was good enough, an automatic setting that would 'lock' in the height when the sensor knows that the bar is level.
Maybe it wouldn't need two lasers, one on each end, but I just thought if it had two, then it would verify that the measuring surface the horse was standing on was level too. If the floor wasn't level, the two lasers would be registering different heights, even though the bar was level. If there was too much variation on the two laser readings, it could show an 'error' message, so you could put the horse is a different place.
This would do away with anykind of uprights that would have to be moved around the horse.
Just a different idea, in case it gives anyone else any ideas.