I found that to be the easy and enjoyable part, ringways aside, when working in Leeds. Is the A650 a viable possibility for you.
Aside for occasional shopping or social event, I have never really had the need to ride to Leeds, as long as I have lived in the area, I've worked in Bradford. But on occasion I travel into Leeds for meetings. Yes, the stretch between the Woodcock and Ringways is a good bit of fun downhill, but not without problem areas, the 40mph limit and pinch points are a problem, especially when you factor in speeding motorists.
Regarding A650 which bit? The ride through Tong Village is OK, but once you've passed the turn off to Pudsey and entered Farnley it get's hairy again. I live 5 mins away from A650 and know better than to ride on it! Its very busy at rush hour and when it's quiet some are driving motorway speeds on it, not one for me! I can take Field Head Lane to the A650, but I take the pedestrian crossing at the end to ride through Drigh moor to join the A58 rather than Gelderd Road, if that is what you were going to suggest. That's even worse as it's 50mph once you've passed the cross roads for Gildersome and Morley. We could really do with a nice segregated route on the A58. There's plenty of room for the most part, not so much on Tong Road or Geldard road. But I won't hold my breath.
