What if you had a bank of UARTs so that any reader could output at any time independent of an other?
Data rata looks pretty slow. How many characters are transmitted at one time?
Another option might be a bank of promini's with a reader attached to each, all feeding back to a master.
Can have quite large tags, and master can collect the data at high speed from each, using I2C or SPI, or wireless even with a little more hardware.
Or hardware serial to master, with RS485 for distance, and software serial to the reader.