"Is the function of the DR and BDR and the other router designations in a local neighborhood really that important?"
Well the idea behind the DR and BDR is to cut down on the amount of traffic between OSPF speaking routers on the same local segment/subnet. So if you have 10 routers all sharing the same subnet with a DR and BDR a full adjacency is only established to the DR and BDR so there is no need for every router to build a full adajcency with every other router which significantly cuts down on LSA exchanges.
Bear in mind also that the DR/BDR are specific to each local segment. So a router that has interfaces in multiple LAN segments could be a DR for one, a BDR for another and a DROTHER for yet another of it's segments.
So whether to manipulate it or not. You would probably want to make sure that your least powerful router didn't end up being the DR or BDR but as long as the device has the horsepower/memory you should be fine. If you like your network to be deterministic by all means configure the 2 6500's to be DR/BDR.
Note that DR/BDR are not related to DR (Disaster Recovery) site at all ie. DR in OSPF simply means the router with the responssiblity of propogating LSA's to all other routers on the same subnet. There could well be multiple DR's in an OSPF area.
The election of the DR/BDR does not directly impact the propogation of routes within your network. So when you lose the HQ connection to the Internet LSA's will be propogated for the change. And each router receiving this LSA will then recalculate its SPF.
The DR/BDR is just an efficiency used for LAN sgements and will not affect the failover to the DR site.
"What significance does the full adjacentcy have?"
A full adjacency is when the 2 routers have formed a neighborship and exchanged their OSPF databases.
Contrast this with the a neighborship which does not necessarily mean a full exchange of LSA's.
I would agree that in the situation that you describe it does not matter very much which router is elected DR or BDR.
There are circumstances in which it does matter who is elected DR. For example if you are running OSPF in an NBMA environment (perhaps Frame Relay multipoint where you have a hub and multiple spokes) it can get very messy if one of the spoke routers would get elected DR. So in this circumstance you very much want to manipulate the election to be sure that the hub router is elected DR.
Or another example: I had a customer (a long time ago) who had an Ethernet segment with a bigger router and a bunch of smaller routers (2500s). Since the DR has to maintain adjacencies with all of its neighbors on the segment it does more work than the DROTHER routers do. So we wanted the bigger router to be elected DR rather than one of the 2500s.
I would say that there are only a few situations in which it matters who wins the DR election. And yours is not one of them.
One other point: I can not quite tell in your post whether you are thinking about the DR as propagating route changes to the entire area or just propagating route changes on its local subnet. As Jon has pointed out, the DR is elected for the local subnet, and each multipoint subnet in OSPF gets its own DR.
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