Usually the problem is to make the antenna smaller not bigger. The wave length of the short distance RFID tags used commonly in price tags and the like is about 22m so an ideal antenna is about this size. Usually an even division of it. If you take a fourth (5.5m) and do a double round, you get a square of about 70cm width and height.
The problem is that antenna design is more of an art than an engineering discipline. The mass of formulas you found shows that it's not an easy task to do it right and it's kind of a miracle to do it good. I'm definitely not a specialist in this area but you can replace the antenna in all RFID readers I've seen yet. I guess your project is feasible but you maybe have to try a lot of antennas till you get a working one.