Increasing the range of a UHF RFID reader
There's plenty of material (academic and otherwise) on this topic.  My light reading of a bit of it suggested that it's pretty straightforward to used a phased array to read RFID tags, but you still need to energize them by delivering sufficient energy in the right band, and that's something that phased arrays just aren't very good at (they have good gain performance for reception, but have no benefit for transmission; you need different types of antenna for transmit gain).

A description of a commercial system that I read (sorry, I don't have a link) talked about using a phased array to read RFID cards at ~300m at a trade show in a big hall, but they had to have an energizer near the card.  I've heard of energizers working at up to a couple of meters, but the inverse square law (2x distance, 1/4 power) is pretty hard to get around for power delivery - you need to transmit massive amounts of power in the right band to get any range out of your energizer.

In your context, part of your range problem is almost certainly that the reason you get only 30-40cm is that's as far as the RFID tag can be and still receive enough energy to operate, because the energizer in your reader just doesn't put out much power.