I just went through this and I documented it here:
Battery Drain in 87 Cabriolet (Or Not?) and here:
Power Window/Power Seat Circuits Crossed?
In my case I found that the power seat and power window circuits were crossed. I believe this was the result of my car's wiring being replaced/molested at some point along the way, so you could be onto something if a PO was "fixing" wiring when removing an alarm system.
My windows worked all the time even with the key out, and even with the power window relay disconnected!
Have you tried disconnecting fuses one-at-a-time and checking window function? In my case I had to disconnect fuses 1 and 2 on block one simultaneously to stop the windows from working. While I was at it, I also solved my fuel-pump-always-runs issue.
I got some great assistance right here on the forum, so you've come to the right place...
Good luck,
GK