I water them with two ice cubes once a week

Stop that, now. It’s an evil marketing trick from the industry to sell you more of their plants.
While you may haven’t killed it for now, the cold shock can severely stress the plant.

Don’t over water it tho.

Best way would be to take it to the sink instead and let some hand warm water run through the pot.

but I’ve not had to feed them or mist them or any of the other things I keep reading online

That’s because most orchids are very efficient in recycling their resources. I would recommend adding a bit of (mineralic) fertilizer. It doesn’t need to be special orchid fertilizer, but it needs to have some micronutrients.

Right now, every bloom is on cost of other parts. You will see the plant decline over time. It will recycle what’s left in the leaves and die a long death.

If you keep it healthy and properly nourished, it will thank you with lots of flowers!

Most comments there say to cut the spikes so it focuses on leaves and roots, but I really don’t think they have enough space for more leaves or roots, and I’m worried that repotting will ruin whatever my streak is with keeping them alive on just ice cubes since that seems uncommon.

Leaves and roots will grow no matter what, it isn’t either/ or. It’s only when forming a massive new spike/ buds the vegetative growth slows down for a while.

If your plant looks similar to the one in the link, definitely cut it. Preferably not directly at the base, but leave one or two unopened nodes so a new spike can form as soon as the plant feels ready for it. That secondary flower spike costs less energy than forming a totally new one and can lead to multiple flowering waves all at once.

Most supermarket Phalaenopsis are hybrids that are made to be blooming constantly. As long as it isn’t weak or something just let it do its thing.

If you prefer to get one single big flush at once, cut it at the base.

Regarding repotting: needs to be done yearly. You probably use bark as medium (the default), which will decompose. If it does, the roots will suffocate and the plant dies.

I personally use LECA, since it won’t decay, but wouldn’t recommend it to you right now, because if you change the conditions too fast the whole whole root system will just die 🤷

Semi-hydro is nice and something you can look into (for example, my plants only need watering every few weeks and flourish! I also don’t need to repot nearly as often), but the transition is stressful.

Repotting is easy if you keep using a similar substrate (bark to bark).
They don’t care if they are overpotted, you just need to freshen up the bark because there are lots of waste products in there.

Look for high quality substrate (maybe online), since regular potting mix for orchids often sucks ass and will decay much faster than a proper one right away.

The comment in that thread pretty much says it all:

You can cut the spikes (flower stems): you will get new, thicker ones that can support far more blooms. Cut them down to the base. The plant will spend the spring and summer growing big leaves, and you will get a great bloom on a new spike starting in late autumn. This is how presentation orchids of this variety are grown.

You can try moving it into a larger container, but I find the roots to be way more sensitive than anything on the plant, so just be very gentle. Bark and Moss mix seems to be the general consensus and not just plain soil.