Ryan, the route there creates the problem...
/interface ipip add local-address=99.173.137.24 name=ampr-gw remote-address=169.228.66.251 /ip route add distance=1 dst-address=44.0.0.0/8 gateway=ampr-gw
You try to push the 44.0.0.0/8 traffic to the tunnel. That traffic belongs elsewhere... The host you are pinging in 44 space expects you to do it via a direct tunnel, not via amprgw.
You need this kind of rules for outgoing traffic: - For src 44.0.0.0/8 to 44.0.0.0/8 it has to go to your ipip tunnels - For src 44.0.0.0/8 to any it is passed to amprgw if the connection originated from the ampr tunnel (connection mark is your friend here). - For src 44.0.0.0/8 to any it is passed to amprgw (I would masquerade to the public IP to reduce de load on amprgw instead of this).
FYI: amprgw does not respond to ping if addressesd via the tunnel, only if pinged from the internet.
Maybe these ideas help.
MArius, YO2LOJ