Dave: your recording shows an 8 bit code. That code is probably store-specific and doesn't match the wheel you were sent. So maybe try all 256 possible codes? Also the installation pictures show just a burried cable (multi-wire actually, so how does that work? Wouldn't the fields cancel out?), so maybe using a speaker instead of a wire with enough current running through it isn't optimal?
Now, if I wanted to generate a signal with all 256 patterns, I'd probably write a program to generate a wave file.. But you have access to fancy function generators. Maybe use this opportunity to demonstrate how they can generate this signal with very little effort? I mean, you keep saying every so often that that part of the value of good test gear is that it saves time.