You're correct in that the schematic shows an LED on both sides of the LDR, but look at the board and you can see that the leads of that photocell stick out the back, just like any normal unit.
Note that while photocells are most sensitive to light on their front, they are sensitive to light, albeit less so, from all sides. The world is full of lots of things that can seem opaque, but still let light through. Next time you measure an LDR's resistance, try measuring it covering the LDR with your finger, and then measure it with your finger on it, but under a table. Under the table, the "off" resistance will be much larger, because less of the ambient light is coming through your finger. Put the photocell "face" down on a table and hold it in place with a piece of masking tape. Now measure the resistance. It will be low-ish, because light permeates both the tape and the seemingly-opaque backside of the LDR. This is why vactrols are larger then you'd think they need to be. It takes a lot of black epoxy to keep the light out and allow them to reach their highest possible off-resistance.
The real mystery for me is why Morley felt the need to light up the LDR from both sides. Was this in an effort to push the LDR to its lowest possible "on" resistance?
Oh wait, I think I get it now....or maybe not. In volume mode, L3 is turned off, leaving only L1 to shine on LDR1, and LED2 to shine on LDR2, presumably in reciprocal fashion (i.e., the shutter blocks either LED1 or LED2, but not both at once), which would be required to produce volume changes. In wah mode, LED1 and LED2 are turned off, which would make LDR1 and LDR2 go high, and function like a large-value input terminating resistor. Is their combined dark resistance too high to provide a desirable tone from the wah? Maybe. In which case, lighting up LDR1 dimly from behind might result in a suitable LDR1+LDR2 resistance to ground.
IN any event, that simply dances around the logic of their use of front and back illumination, and doesn't really tackle why the pedal isn't working properly.
BUT, having said that, is the shutter itself aligned properly? I know it is misleading to judge from the single photo provided, but it looks like the shutter might be rubbing against, or even maybe blocked by, the PCB on the "lower" edge, where L2 and LDR2 are situated. I don't expect anything to be burnt out during 20 years of storage, but stuff CAN get jostled and repositioned, and as delightfully crackle-free as Morley's system is, the positioning of the shutter, light source, and photocells IS critical to their proper functioning.