'pruinosus' with a 'us' at the end to be precise. I have one of these. They're columnar, so it should eventually grow more tall than wide, and I believe overall much larger than Astrophytums. Mine has always been indoors with as much sun as possible, and it's at least 8" tall now and decently shaped.

..."Since the rains started here I have lost several cactus"... Isn't initial problem too much rain that possibly caused rotting that attracted bugs of any kind? Just like a flies/grubs feeding on decaying flesh (or even fresh, uncallused wound)...they didn't cause death of it, but certainly take advantage of feeding and laying eggs on their favorite...Too much rain could be the reason, and larvae or any bugs (likely laying more eggs!) a consequence of it. I would assure all succulents are in very fast draining mix, in containers with excellent drainage (holes) and if rains are persistent, perhaps use some extra rain protection. Even just an outdoors umbrella helps, or if many plants, plastic sheet or similar temporary protection.

I use motion detecting sprinklers for 6 tables of plants on my roof, which has worked fantastically. They don't even go around my plants when the sprinklers are off (in case I left them off by accident). I know someone who has live trapped and relocated from their property, but from what I hear squirrels are very territorial and others will just move in. They had to modify the traps slightly for higher sensitivity because the squirrels/chipmunks could get in and out. One day they also caught a bird!

My cactus get low's in the low 50's in the winter. I have the greenhouse thermostat in the winter set to about 52/53°. On sunny days it gets quite warm. I don't want it colder than that because I have my Adeniums in there. Anyway, the cactus flower fine. I do question whether grow lights would be bright enough for summer growth for the cactus to grow well and flower. Maybe there are led fixtures that would be bright enough. Don't know, have never tried it :-)