I went through this exact spiral a couple seasons ago. Shocked, waited, tested, shocked again. Water wasn’t green, just that stubborn gray haze that makes you wonder what you’re missing.
If you’ve hit it three times and there’s still no visible algae, I’d stop thinking “kill” and start thinking “clear.” At that point it’s usually one of two things in my experience: either you’ve got a ton of dead organics still suspended, or you’ve pushed the water slightly out of balance while shocking repeatedly.
First thing I’d check is combined chlorine. If CC is still above 0.5 ppm, you may not actually be done oxidizing. But if CC is low and free chlorine is holding overnight, then it’s more of a filtration problem than a sanitizer problem. What’s your filter pressure compared to your clean starting pressure? If it’s 5 psi or more higher, the filter could be loaded up and just recirculating fine debris.
Also look at calcium hardness and your overall saturation index. I once overshot shock with cal-hypo and my CH climbed enough that the water stayed cloudy even with good chlorine. It wasn’t scale on the walls, just microscopic precipitation floating around. Took dialing pH down slightly and giving the filter time to polish it out.
When mine did this, the fix ended up being: deep clean the cartridges, run the pump 24 to 48 hours straight, brush twice a day to keep particles suspended, and stop adding more shock unless testing actually showed a need. Cleared up in about two days once I let the filter do its job instead of throwing more chlorine at it.
What are your current numbers for FC, CC, pH, TA, and CH? That usually tells the real story.