I am a fabricator. It distresses me when someone goes thru an experience like yours because the stone supplier or fabricator did not accurately communicate the material properties of a particular stone. In my shop we make CERTIAN a customer knows the properties of a stone they are considering including signing off on the details because we don't want that unhappy customer coming back a few months down the road. "soft quartzite " doesn't exist. If it's soft (and etches) it's marble and has all the performance deficiencies marble is known for. with Real quartzite is so hard it's a challenge to process in the fab shop which is part of the reason it's considerably more expensive. For your application the only long term option is to replace the top with any one of hundreds of options in natural stone that will hold up to your planned use with little or no maintenance.

I had answered like 2 hours ago, but, it didn't post!!! Grrrrr. OK, Mariy, you could do as Rina stated and cut above the wound, let cut dry a few days and place on the surface of growing medium and wait for roots to grow out the bottom of the top cut. Many growers often start new plants this way. You could, also, just let the wound callous without surgery. If the roots are still viable, stem is not soft, liquid plant is not leaking out and it's not squishy, the plant may very well heal and grow over the cut area in time. Not sure from the pic, but, it looks like the center of the stem is exposed and there is rot. If so, I would cut off all the damage and try from there. The regenerative powers of cacti is astounding, to me, at times. I've developed a keen respect for these prickly spheres. One of my cactus was bit into a crescent moon shape by a dumb dog once. It took all summer, but, it healed and grew over the wound as the wound decreased until the plant was roundish again. Another of my cacti lost more than half it's mass from dry rot (there's a thread somewhere on it) and stood in green suspended animation (Umhm, we all know how fast cactus grow, but, this was even slower) for 2 summers. It has now produced a healthy new pup that's growing quite large and fast these last 2 months. In either case, I would let that wound completely dry before potting up. Leave it somewhere protected from moisture until it does. For any cuts I apply powdered garden sulfur as it's an anti-bacterial/fungal. Works really well on cacti and orchids. I don't have experience with this, but, some folks on this forum, use cinnamon as a cut protectant in place of the sulfur. IMO, your plant has a good chance of recovering. Hope this helps.

Pry the flower and glue off. By gluing together the top of the plant, which is where the new growth comes from, the plant's ability to grow normally is severely restricted. You can see that in the picture- all the little bumps are being pulled together instead of spreading apart as the cactus grows. I've had good luck gently and slowly prying up the edges of the glue so that it comes off without too much damage to the plant and spines. If you can't get a grip with your fingers because of the spines, try tweezers. Sometimes, though, the glue just won't come off the spines and I have to snip them with scissors. I try very much to avoid any damage to the plant body itself (the green part). It looks like it's in a very peaty mix, so yes, repotting would be a good idea. A good starting place is to mix commercial cactus and succulent soil 50:50 with perlite to get better drainage. If you search on here for "soil mix" or "gritty mix" or "why is my cactus not doing well", there are a ton of threads discussing this. The good news is you've kept it alive for four months! Great!

Oh boy this sucks;)! Euphorbia ingens are cold hardy down to about 28F. So from now on these will need to be protected during the coldest days and nights. I think you've learned that lesson;). Somebody should have made you aware of this when you purchased them. You live in a zone where the temps get down to 10F-15F so the seller should have least tried to sell you frost cloths at the time of purchase. I'm sure those Euphorbias were not cheap. This is tough a one because they're big and the pics aren't very clear. So it's hard to tell what's going on. The areas that look bad are they mushy? Regardless if they are mushy or not there is frost damage. The growth tip is destroyed. So those parts will no longer grow, but will branch on the sides:). So one of two things will happen or a little bit of both. The areas that have been damaged will either dry up like this. The above pic shows frost damage on my Euphorbia grandicornis from last winter. See how the damage just stopped and dried up. I probably will cut eventually. Or the damaged areas will get mushy and spread. Luckily your Euphorbias are on the bigger side so you can kind of wait and see. Keep a close eye on them. Watch for changes. I honestly wouldn't chop quite yet. Wait and see how things play out. If you notice things take a turn for the worse you will have to cut:(. E. ingens can take temps down to 28F, but for most of my plants I don't like to let them go as low as they can go. At least without some major protection. Any growth tips you see that don't have any damage cover with styrofoam cups or similar. This will help protect them. Heck I would even cover the damaged tips;). Then cover with the frost cloth. I know I didn't give that much advice, but this is exactly what I would do. I just think if you go and chop now it may be a little premature. I mean there is definitely damage, but I would just wait and see what the Euphorbias will do.