That's quite a dilemma you have all factors considered, and 3,000 square feet of space is a lot to handle, but it can be done for less than you're getting quoted. For the look that you are after, epoxy is actually not all that bad of an idea because you can sprinkle flakes on it to get that terrazzo look. However, epoxy is considered more suitable for an industrial setting like the interior floor of a car dealership or for the floor of a garage. One reason is because of the off-gassing of the chemicals in the epoxy that can compromise your home's air space. The epoxy can also turn yellow over time, especially with white! However, it might be something you'd want to look into more and talk about with experts to get their take on it as it would be a relatively inexpensive coating compared to others you've considered thus far.

I'd stay away from stained or painted concrete. You'd need stress valleys cut every so often to prevent cracks, and stained concrete with a coating just isn't as durable for a long-term surface in a home as you would want. I think the maintenance on it is fairly high. There is a recent post here at Houzz where @SJ McCarthy who is a flooring expert commented on the stained concrete look inside of homes and tried to steer someone away from it for several more reasons. That said, I have a relative who did a beautifully variegated stain and finish on bare concrete for a ranch house, and it looked beautiful. If for some reason you do more research and think you want to take the plunge, then be sure to get an accurate quote on surface preparation because that will be the key.

Marmoleum is a fun surface, and I considered it for my own kitchen and have seen samples in person. It was a popular flooring selection among the old Garden Web contributors who posted here before that forum merged with Houzz, so you can still find a lot of posts in the archives about it as well as a few comments from people who have used it more recently. My conclusion from studying dozens of reviews was that it is great in the short term for a flooring, but it isn't going to last you for decades. It can also stain. If you plan to be in the house a long time and especially if you have heavy furniture that gets moved around periodically, this is not the flooring for you as it won't hold up to your usage requirements.

There is cork flooring, carpet, tile, hardwood, LVP, and linoleum, but again I know you're trying to aim for that terrazzo look. it's possible to catch sales on great products like from Porcelanosa and get quality tile for around $4 USD per square foot. That's about what we paid for a marble-look "Thassos" tile from Porcelanosa during their 40% off fall sale last year. If you order tile through ProSource, you'll also get good discounts. The labor on this is what will impact your budget. I'd shop around for installers to see if you can get better pricing. $10,000 for removing 3,000 square feet of tile sounds a bit high unless that includes sub-floor prep too. Some of that cost is going to be their transportation and dumping fees for the waste, but still, that sounds high to me, and we just had a similar project done over a smaller area. If you find a local craftsman who doesn't come through a company that has to pay overhead costs, you'll get the best labor price going direct.

The $10K quote for removal is roughly $3/sf for removal. It is entirely possible this is in the ball park. The type of tile installed and your location will dictate the cost of removal (some areas are VERY expensive to pay for work whereas other areas that are SUPER cheap). In an Expensive city in Canada, a $3/sf removal of tile is a snick high but not unheard of.

Linoleum is an excellent option - but make sure you realize the amount of MAINTENANCE you must deal with. Real lino needs polish/wax. With 3,000sf of flooring, you are going to need a VERY good polishing machine. Polish also needs to be removed every 5-6 years.

A cork floor will offer the MCM look you want. It fades HEAVILY and turns to a 'bleached blonde" colour (Gwen Stefani or Marilyn Munroe hair colour). A floating floor would be your best bet for cost ($4-$6/sf for material + $3/sf for installation). That still puts you in the $10/sf for your home.

I would check out the best terrazzo-look tiles. Look at large format, rectified. I can’t seem to post pictures from my screen, but Emser has a “terrazio tile that looks very nice. I think this option would look waaaaay better than garage floor material.

Some type of stained and polished concrete might work. There are toppings that can be applied to existing concrete subfloors that will give a clean finished look.

https://www.youtube.com/watch?v=0zLRRlMkFsk#:~:text=Ardex%20PCT%20polished%20concrete%20topping,for%20new%20or%20existing%20concrete.