I would accept as an answer specific details about which second hand machines don't have this problem. I've looked at various feeders and am finding that it looks like many of the 'high end' feeders might have this same issue since they have a pretty tight diameter waste tape path.
To follow up to myself: I found a picture of a 32mm panasonic feeder as an example, and it looks like the exiting tape may go toward the middle of the machine. So I guess I need to add a question here:
How does the tape exit these feeders, and where does it go?
On my autotronik, the waste tape makes a 180* turn and then comes out of the bottom of the feeder back towards the operator. Because the pick lockation is pretty close to the end of the feeder, there isn't enough room between the pick location and the end of the feeder for the tape to make the 180* turn with enough of a radius that the 32mm tapes can actually make the turn. A thicker tape, like those used with RJ45 connectors and the like would only be worse.
I'm assuming the higher-end machines have worked through this problem, just haven't used any with these large of tapes to know if they would have a similar issue. Same with some of the low end machines, although I do know some of those kick out their leftover tape toward the pcb working area.