I don't have the answers re: vermicomposting aspects, but for cat aspects:

Be careful with fuel pellets. Make sure they have no additives and are ONLY sawdust, otherwise they can have potential health consequences for your cats over time.

Pine pellet stall bedding for horses is basically the same thing as expensive litters like Feline Pine at a much cheaper price and won't have potentially toxic chemicals in it. It also should be available year round.

Potting MIX (soil free mix) should be fine for cats as long as it's free of added fertilizers, etc. However, I'm not sure it'll be that cheap over time. The nice thing about the pine pellets is that you know which parts are soiled and can sift that part out and keep the whole, unsoiled pellets in the box. It's probably much harder to know what's soiled and what's clean in a box of potting mix. Although cats do adore anything with a real dirt-like texture in the box.

For the last 4-5 years of our cat's life, we used stove pellets as cat litter, and it was absolutely the best litter we ever used - and cheap!

We'd go through a little more than one bag per year, and where we are, the pellets are well under $10 per 40lb bag. Until we found a place or two where we could get it year round, we'd
plan on buying 3 bags during winter, just to keep the bedding situation
under control.

We also found that the bedding would go twice as long (usually more than that) between cleanings. NO smell! Once we started using the pellets, smell ceased to be a problem ever again. In addition, we used what looked to be a pitiful amount with each refill, and it would break down into a whole litterbox of filler.

When it came to catbox changing time, we'd dump the current box into a far corner of the back yard, away from people. We'd rinse the box out with the hose before bringing it back in, and hit the pile with some water to start the composting process. Then we'd pour a little less than 1 qt of pellets into the box. The water leftover from the rinse would get soaked up by the pellets in a minute or two, and they'd start to fall apart. If that wasn't enough fluff, I'd grab a spray bottle and hit with a few sprays to encourage a few more pellets to give up.

After that, the box wasn't wet any more, and there was enough fluff to make the box acceptable to the cat. As she used the box, more pellets broke down and provided more fluff, filling the box completely. Cat was happy.

Meanwhile, out where we dumped the cat litter: Occasional waterings and rainfall would make the sawdust and urine and cat poop start to break down. Somewhere along the line, we'd pile up more used litter, and at some point, the pile seemed to stop growing, because it would break down into nothing as additions were made on the top.

Once in a while, for the heck of it, I'd get a shovel and turn it all over into the dirt, and we'd start over. It was all pretty brainless.

I think using cat litter in the vermicompost bin is not recommended due to the pathogens that can be in the cats droppings due to a mixed diet. I would do more research on that before attempting to add it to your bin.

If you do what priswell is doing and putting it in a compost pile that heats up it should be fine. Granted I cannot get a cat due to allergies.