Would it make sense to do the same setup as Bruce Abbot proposed (first regulator and then balancer/protection board), but to use a charging circuit like BC3770 instead of using a regulator?

The BC3770 would (as far as I understood) have sufficient power to charge all the 4 cells and it would be a lot "smarter" than just a regulator (trickle charge for deeply empty batteries, top up charge etc.)

Datasheet:

http://www.nxp.com/docs/en/data-sheet/MC32BC3770.pdf

What do you think?

Would it make sense to do the same setup as Bruce Abbot proposed (first regulator and then balancer/protection board), but to use a charging circuit like BC3770 instead of using a regulator?

The BC3770 would (as far as I understood) have sufficient power to charge all the 4 cells and it would be a lot "smarter" than just a regulator (trickle charge for deeply empty batteries, top up charge etc.)

Here is a link for the MC32BC3770 Datasheet