It looks like in order to bridge using GRE, you have to use the EoIP interface (which basically uses GRE anyway).
(bridge won’t let you attach to a native GRE interface)
So don’t worry about trying native GRE unless you want to start using routed connections (I would personally use routing, actually, if this were my project)
As for EoIP - have you tried to create an IPSec connection from your home router to the CSR - your classifier could simply be GRE between the two sites. - If you can do that and leave your standard EoIP configuration in place but protected by IPSec, this should answer the question about whether the ISP is causing this problem.
An interesting coincidence, someone just posted a solution to decode inside of EoIP tunnels using wireshark:
http://forum.mikrotik.com/t/eoip-wireshark-dissector/86333/1
It works great, and might help completely verify if you see the correct ARP / Reply on the physical ethernet itself.
(you can just filter the display to show arp)
I set up an EoIP tunnel in the lab here and filtering for things inside the tunnel is very easy now.