My first response would be to say no....
As a inspector, I have to view remodel installations carefully, and a shared neutral from multiple circuits on different phases would be problematic at best, and that should be confined to the distribution panel. What you want to do is use the neutral buss in the old panel and splice in new feeder hots from the new panel.......pretty sloppy would be my first impression.
Splices, if done neatly and in NEMA approved boxes that are accessable for the application is what I look for.
I would have you remove the old meter and panel box. bring your new feeders into the home and junction them, assuming the wire you were tying onto was of the same size and had grounding conductors. Or, install a Nema approves splice box....NEMA 3R, of the appropriate size, and splice each feeder, The old box, once the harware is removed, can not be depended on to be weather tight.
What you have done or are doing is going beyond the simple meter replacment or panel replacement which would not generally entail the replacement of the entire branch circuit.
Once you replace a feeder, then you get into a number of code compliances that you must meet, and grounded outlets, GFCI's, AFCI's and the like all come to mind.
I try to be reasonable on remodels, and I can't say that I might approve a number of different ways to tackle this problem, so I'm giving you the range of things that might be necessary. There are a lot of variables that need to be looked at.