Broadcast Packet Issues

OK - I've got an interesting situation, and I'm looking to see if anyone's got any ideas how I can work this out.  I feel I may be pretty out of luck.

So, a quick run through of everything.  I've got two buildings my HQ and Remote.  These two sites are connected via an MPLS\PNT circuit, that routes between buildings using our Private IP space.  Easy enough.  

The part that becomes tricky, is the IP address space we are using.  NOTE: This was an inherited setup, and I would have never had assigned my subsets this way.  So, my HQ network is based off of a subnet 192.168.0.0 mask 255.255.240.0.  MY Remote subnet lives in the 192.168.1.0 255.255.255.0 subnet.  Obviously, the remote subnet lives within the space of my HQ's subnet.

So, my problem - We are seeing enormous amounts of Broadcast traffic going over this MPLS line, and crippling the speed (it's only a single T1 1.5 Mb circuit).  So I want to not allow broadcast traffic over this line.  Changing the remote locations subnet is currently not an option (I do not have anyone in that office capable of helping with such a task).  

The solution I can think of is to build out a VLAN for the link.  Currently my routers are as follows:

192.168.1.0 use 192.168.0.7, where 0.7 is the routers LAN interface.  Also note I DO NOT HAVE ACCESS TO THESE ROUTERS, they are MIS routers managed by AT&T (another thing I would have not done).  

So as far as I can tell, creating a VLAN and adding the uplink to the router to that VLAN would kill the broadcast packets.  Only problem, is that I can't create a VLAN that has a subnet that is within the subnet of the default VLAN, not to mention that the IP address of the router is in my base VLAN as well.

If I could make the subnet change, I'd do something like:
HQ Router: 192.168.50.1
Create a VLAN: 192.168.50.2
Remote Router: 192.168.51.1
Remote Subnet: 192.168.51.x

Then create the route
192.168.51.0 to use 192.168.50.1


Suggestions?  Am I just screwed and will have to re-evaluate my entire IP structure(which I will be doing anyway, but not planned until later this year)

JJ