Hi Mark,
yes this post is even too long for bed time reading now!!
the description and codes point to a weak compressor,
but 1st, does the car sink when left at level 1?
if it sinks to the bump stops then you still have a leak, most likely an airbag
for the compressor:
the air escaping from the high pressure relief valve area (white cap) is strange, does the air constantly whoosh when the compressor is running?
has this 2nd hand compressor ever worked?
if someone has opened this compressor previously they may not have fitted the valve correctly if it has never worked, if air constantly sounds/leaks out when the compressor is running, try to trace where this air is coming from, using soapy water or listen may confirm actually where the air escapes from..
OR- (just a thought!! & more likely
)
if this ONLY happens during the output tests the software may open the n111 release valve on the compressor to vent the air out so the compressor is being tested to run, not for pressure. if this is the case the air will be passing out through the large plastic "bent" pipe next to this "white cap"
perhaps to confirm this air escaping noise, best to check when the car is requested to lift normally (press up) the compressor should start and then listen to the compressor to see if the air leaks out. if no air leaking from the compressor or the front airbags, get a kit fitted to it,
best regards
Andy