Agree with last poster, data is valid on negative edge of clock, otherwise there is no setup. Your 52,85,0,7F should be A1,85,0,7E.
Here are my guesses- play around once you get Salae capturing proper clock edge.
The A1 might be an address or a preamble- do all strings start this way?- "A"-1010 is somewhat common here.
The 85 is likely a command (up / down? )
The 0 is the data payload (one of the messages captured had a 20 here and 4th byte (cksum) changed by that amount.)
The 7E is a checksum though I don't know exactly where it starts and what gets summed- it seems to be a simple sum vs. a CRC, etc.
Map out how many "states" the controller can send by experimentation.
A few buttons and a 35 cent micro could and usually does implement something like this.
The slowing down of sending data is an "non active" or "idle mode", it lets all the power stuff just turn off and hold position to keep heat down. If you're messing with the buttons, it will stay up but will then time out. It could be that the first data with the zero payload is a "wakeup" and is ignored.
Notes-
5's and A's are generally good 4 bit numbers to use in binary protocols- they are 0101 and 1010 as binary nybbles. AA,55,A5 and 5A are common.
The above can capture some common errors where the bits can't flip high and low at the right speed.
Zero's are often used for null data payloads and sync bytes esp with cksums - they're not great because they don't change... middle of packet only
The control scheme may send 0, positive or negative (2's comp) type values - "0" Wake Up, do nothing "+" Go Up x units "-" down x units
All just guesses- have fun. Have you looked on line for anyone that may have hacked in the past?