The tee you installed is for the supply line to the RODI, but you still have the sink getting its cold water supply. So, the clean look would not work with that set up (sink still getting its cold water supply). If you did want the water from the blue line to come out the faucet, the cold supply line would only feed the RODI unit, not the sink too. So, after the cold water valve you would need a reducer going only to the RODI. Then the blue line would need a similar fitting to connect to the faucet supply line. But, your clean filtered water would now be going through the metal faucet fixture/shutoff valve (copper/brass) and possible introducing metals to your RODI water. I would not do that.
Keep what you have done. Then add inline ball valves on your supply line going into your RODI and then one at the end of the output blue line. Mount the RO input valve near the door for easy access and the output line valve on extra line to pull out and fill your bucket.
EDIT: Philip beat me to the punch with a picture. Just have a ball valve near the end of the blue output line. Easy shut off at bucket