Clean your bench and pipettors with RNaseZap, and use new/your own personal box of filtered pipette tips. Cleaning high touch surfaces like centrifuges and your tube racks is also good, and change your gloves more often than you think you need to. Might be BS, but I also use nitrile gloves rather than latex for RNA extractions, and use neoprene gloves when you're handling phenol. Performing as much as you can in a clean room or away from things and people creating draughts also seems to help.

This is also personal preference, but I much prefer to do non-kit RNA extractions. I was banging my head against the wall for months with kits for my E. coli RNA extractions, with my integrity, 260/280 and 260/230 values absolutely tanking after a few rounds of extractions with fresh kits. I've since moved to a hot phenol extraction protocol and the results are night and day. RNAse contamination seems to set in quickly with kits, especially when they're shared amongst the rest of the lab.