Sergio, why are you worried about the "width" of the DAG?  I would think that every miner is incentivized to extend the "tips" of the DAG.  It really comes down to the metric for "work".  Bitcoin's measure of work is extremely simplistic because of its linear structure.  With a DAG you're looking at the "work" in the set of transactions upstream of the current transaction.  If miners "widen" the DAG, they are not contributing work...all the transactions have the same amount of work -- that of themselves plus their parent.  So this seems easy to solve by computing "work" in a smarter way.

I have a couple of preliminary formulas for calculating work in a DAG under certain constant-target assumptions that eliminate your concern, I think, but I feel there's still a better solution I haven't found yet.  I also want to get rid of the target difficulty and simply combine whatever hashes show up.  (This then frees "difficulty" to be a node-specific quantity that can be used for bandwidth control and DDoS protection)

In case you haven't seen it, I propose the same thing (DAG-chain) here:

http://blog.sldx.com/three-challenges-for-scaling-bitcoin/

I have a longer draft with a lot more specifics on the DAG/braid concept that I'm not ready to publish just yet.  Only as of last week am I paid to work on bitcoin, so can actually bring it to fruition.  We should see if we can collaborate, feel free to contact me privately.