The Pitch Pirate uses a 100K Delay control in parallel with a 100K Depth control, so the overall resistance is the same as having a 50K pot on Pin 6 of the PT2399 - pretty standard stuff.
The LDR hangs off the Depth pot's wiper down to ground, so any LDR that has an on resistance that goes down close to 1K is going to be good. That provides plenty of options, since most of them do that. If you're not getting enough "On" from your LDR, perhaps the LED isn't being driven hard enough. The raw TAPLFO output can only source 20mA, so don't try for more than that from the chip directly. If you need more current to bring the LDR resistance right down, use the TAPLFO output to drive a transistor and use that to drive the LED. There's an example doing the same thing with the STOMPLFO in my FilterFX schematics:

(from
https://electricdruid.net/filterfx-lp-bp-hp-lfo-filter/)
Some vactrols can handle quite a bit of juice. The VTL5C3s from Xvive are spec'd up to 40mA, for example, although I've never bothered driving them that hard. The circuit above uses <10mA for example, but I didn't need super-low resistances, since I could lower the cap values in the filter instead.
I recommend sticking a multimeter on the LDR to measure the resistance, and then using a 5V power supply with a few selected resistors to see what output resistance you get for what LED current. Either work out the LED current using the LED forward voltage (Vf) or use one of the online calculators to do it for you, or alternatively, use a second multimeter in series to measure the current flowing through the LED. Or both, why not?! That'll give you a decent idea of the sort of LED current range you need to cover. The "off" end will go to some stupid-high value over about 5 minutes, but won't matter much because it's in parallel with something that's only ever going to be 50K. The "on" end is what makes the difference, and that depends on the maximum current that the LED sees as much as on the LDR type.
If anything here's not clear, just ask.
HTH,
Tom