There aint diddly dick in between Bryce and Zion...
And getting into Zion from the north entrance, while absolutely beautiful(especially compared to the south entrance), takes an hour to go like 16 miles plus your time at the entrance gate...plus your driving time from wherever you stay in between Bryce and Zion... I would only want to go in the north entrance once...
Head to Bryce from Moab(5 hours give or take if you run the route through Capitol Reef(moab to I70 to 24 south to Torrey then pickup 12 to Bryce)) and if you leave by 8, you will arrive at Bryce by 2(with an hour set aside for lunch) which gives you time to hike the Figure 8 or Navajo/Queens Garden or hit the overlooks and GTFO... Stay in Bryce at Ruby's and bounce to Zion the next day. OR if you want to take your time getting from Moab to Bryce(and stop at Goblin Valley, Capitol Reef(get a pie), and a few overlooks while going over Boulder Mountain towards Bryce), still stay in Bryce at Ruby's, get up and do your hiking/overlooking the next day in the morning then head the 2 hours to Zion that afternoon. I guess what I am saying is 1/2 a day or maybe slightly more at Bryce is plenty unless you are going to do the 8 mile Fairyland Loop trail(which sucked compared to the Figure 8 or Navajo Queens garden trails which can be done in 2 to 3 hours)... I would plan to spend more time at Zion vs. trying to stay in between and shuttling in between, which isnt worth it. You will be done with Bryce in half a day or so and then be pissed you are driving like 1.5 hours to get into Zion and battling that traffic into the gate for the other full 2 days...
Again just my opinion after having just been out there 2 weeks ago.