As you observe HSRP has to do with which gateway the end stations use and HSRP will influence how traffic leaves the network. But HSRP has no concern about how traffic returns and has no influence over how traffic returns.
If Symantec applications are sensitive to this, then I think that you need to look for a solution in something other than HSRP.
One workaround would be to alter the routing metrics (whether it is a dynamic routing protocol or is static routes) so that the remote networks prefer the path through the router that normally is the active router. This would fix the problem while that router is active. It probably would create a problem in situations where the standby router became active.
I am not aware of a good solution that can modify the routing decision for return traffic based on which router is active. (Though it does occur to me that there might be some possibility in the new object tracking capabilities in recent IOS for the remote routers to track addresses on the HSRP routers and perhaps modify their routing in response to whatever makes the primary router fail over.)
HTH
Rick
HTH
Rick