On the issue of HSRP at site B, it's really only necessary for site B router, or its LAN interface, failure. Assuming the two site B routers OSPF peer, and they "know" the other router's routes, OSPF will reroute traffic from the primary gateway router to the secondary path. Certainly HSRP tracking can move the gateway to avoid an extra hop, but also assuming the Site B routers LAN interfaces have (much) more bandwidth than the WAN, the extra router hop (during primary path failure) shouldn't be too much of a concern.
In a later post you mention these routers also support the Internet. In that case, you might want to consider making one the primary path for internal traffic and the other the primary path for Internet traffic. This allows you the option to manage internal path bandwidth since, excluding one path's failure, you'll have deterministic available bandwidth for internal usage.
For such a setup, you could continue to use HSRP at site B, and one type of traffic will normally get an extra hop, or if site B routers support it, use GLBP and half of traffic would get an extra hop. Also if device supported, best option might be mHSRP so that traffic would be redirected to best virtual gateway.
PS:
BTW, when working with your tunnels, highly recommend, if device supported, the mss adjust command. You'll also want to insure PMTUD is working correctly.
