When light hits the LDR, its resistance drops and the current through Q418 increases. This causes the collector to drop for its nominal voltage of 5.1 v (no light) to 1.6 v (full light). This 3.5 volt dip in voltage is coupled through C217 to the base of Q417. The *length* of this pulse is dependent on the value of C217.
Q417 is normally held on by the base current through R443. The negative going pulse from Q418 turns this transistor off. When it turns off, it allows C416 to charge through R442. When the collector gets high enough, it couples a positive going pulse through R441 and a diode into the circuitry that controls the solenoid.
If the run switch is not in the 'play' position, or the switch is bad, then the base of Q417 is pulled high harder with the 15K resistor R444. This has the effect of reducing the width of the pulse coming through C417 to a value too low to produce the required output pulse from Q417.
So, I can see a number of scenarios where manually moving the tone arm quickly will cause the solenoid to engage, and moving it slowly will not:
1. Something incompatable with the replacement LDR. Its resistance may be changing too slowly with the change in light due to mechanical variations or orientation.
2. Capacitance of C417 too low - this will reduce the pulse width passed on to Q417.
3. Capacitance of C416 is too high or it is leaky. This will increase the length of time Q417 must be off before the collector reaches the 'trigger point'.
Confirm any changed caps are installed with the correct polarity. In the schematic, the cup shape is the negative end of the cap. So negative end of C417 to base of Q417 and negative end of C416 to ground.
Confirm that the value of C416 is 3.3 uF and not more.
Confirm C417 is 22 uF. You could try increasing this. I would try a 47 uF (or just parallel the installed 22 uF with another 22 uF).