Hi Chris
First of all, sorry for the incorrect reference - it should have read P5 not IC5. I am afraid that my notes were wrong and they have now been corrected - well spotted.
Bad news that the adjustment of those screws hasn't fixed the problem. I therefore conclude that the arm is arriving in the correct cueing position and stopping. At that point, there should be a signal from the micro telling the arm to lower. I would check that out next, P6.18 should go high if the micro is telling the solenoid to work and P3.1 should go to 5V or thereabouts. If the voltages change then the micro isn't the problem. If the voltages change and the arm doesn't lower then we would have a mechanical issue. However, considering that when you press PLAY this sequence does work, I would expect to find that the micro was not sending the required "lower" signal. In that case it must be getting confused for some reason and that could take you back to capacitor problems in the power supply.
On another occasion, I had some problems with this start up sequence and it turned out to be an excessive amount of ripple on the 5V power supply. This was fixed by changing the large 2200uF capacitor, C24. If you wanted to limit the amount of caps to change, I would check the characteristics of the 5V supply with a scope and change capacitors C24 and C20 to make sure that the micro was getting a good reset signal.
Keep looking and you always find the problem
Regards
Geoff