I have very similar setup and same problem. This has nothing to do with default routes, as at both locations they always shall point to external world in order to route hosts traffic to an internet. “IP ROUTE (remote_lan mask remote_site_Firewall_IP)” is essential for communication between site_A and site_B hosts.
In our setup all of this works just fine, but you do not have access to hosts_B if you VPN to Firewal_A (SAS-5520 in our case). By default setup CISCO does not rout VPN traffic to any remote networks. The VPN connection is limited only to a network physically connected to a Firewall and also gives you Internet access (over tunnel). I can understand why it is the case, when you have site-to-site VPN tunnel between Site_A and Site_B. CISCO could claim if user want connect to hosts at the other site – establish new VPN connection to that site. Inconvenient I could say, but doable. But in our setup we have remote (from the site with ASA appliance) network connected over point-to-point dedicated corporate channel.
I have played with all possible combination of routs and access lists and could not figure it. I will very appreciate any ideas or advices.

Bets regards,
Dmitry.