So just make a bunch of patch cables with RJ11 for phone side and RJ45 on wall side if the RJ11s don't fit snugly into Cat 5 ports. It was a dream to move into a new apt where all phone/data ports were RJ-45 so we could assign the ports to whatever purpose we wanted.

OnQ and others make break-out boxes/dongles that you can plug into 568A-jacks and assign to phone 1, phone 2, phone 3, 4 ... or any combination thereof (or leave as data).