We've been through recurrent blockages with our boy.
Did they actually confirm crystals were the cause of the blockage, and not just that they were present? We had a referral to a specialist, and despite crystals being picked up in the sample and our vets indicating it was the cause, some crystals are completely normal and in our case it is stress-related spasms.
Given the house move you describe, this could well be the case for you. In which case, reducing the stress will be key.
Re diet, prescription foods basically increase the ph in the urine and contain low levels of phosphorous and magnesium.
There are diet tweaks and supplements you can give to create the same effect alongside raw/homecooked or even wet food - daily cystese alone didn't prevent blockages with our boy. Uri Balance/ Uri Care can be given short term as an acidifier but we're also now using Urinary Gold from Amazon. If he uses a litter tray you could ph test the urine to make sure it's not getting too high (crystals form in high ph), if this was indicated as a cause by the vet. We now test daily.
Alongside reducing stress, the biggest thing you can do is try to increase water intake. Like you, we had a battle as he's NEVER drank water, despite many different foundation, cups, bowls, you name it... We added extra water to his food, but again, this alone wasn't enough to prevent the recent blockages. He's now on a homecooked diet (with a completer) and we keep boxes of the broth from cooking it which thankfully he will lap up.
Juice from tuna (in spring water not brine) also gets recommended but imo there's not much per can plus there is also some research on a link between fish and cats with bladder problems, so we tend to avoid for that reason.
There are a couple of really great facebook groups for advice too - one called feline lower urinary tract and another called feline nutrition - feed cats like cats.
Unfortunately there are a lot of us out there battling these conditions, but there's also a lot of advise too.
It's a horrible condition for cats and you have my full sympathy trying to navigate this.