Well,.. let me see, if I can address your queries one by one.
vSphere distributed Switch is a VC feature. So once you change a VC, the related DVS will be lost or the reference of the DVS object will be lost in the VC.
Once you add the Hosts to a new VC, the hosts will still be looking for the DVS object, however, the DVS in your new VC will be having a new reference. So yes, you need to add the hosts back to the newly created DVS which will result in downtime.
Is this correct, or would the host somehow import the vDS into the new VC? I think this is unlikely.
I have not seen or used an application which would help us transition to the newly created DVS. It might be a new idea which you can work on
Theoretically I would be moving from one vCenter 5.1 server to a new vCenter 5.5 server.
I would suggest to recreate the DVSwitch config to 5.5 and add the hosts, since there are a lot of new features in 5.5 DVS vSphere 5.5.
Hope it helps,
zXi