Same subnet on two interfaces

I need to support kind of a strange setup that I'm not sure how to configure correctly:

My network setup is like this:

              [                          SRX345                          ]
10.0.0.3/28 --[-- 10.0.0.2 @ ge-0/0/15.0 -,----- irb.1 @ 10.0.1.254/24 --]-- internal network
10.0.0.7/28 --[-- 10.0.0.6 @ ge-0/0/14.0 /

Default route to the Internet is via 10.0.0.3. I'm receiving additional routes via BGP peer at 10.0.0.7. I need to advertise my routes in 10.0.0.0/28 back to 10.0.0.7. I have a static NAT entry for 10.0.0.4 <--> 10.0.1.1 and a source NAT from 10.0.1.0/24 to 10.0.0.5. SSH and IKE to the router needs to be accessible at 10.0.0.1 from both external interfaces.

I've tried configuring this in various ways including /31 subnets on my interfaces, /28, proxy-arp, unnumbered interfaces, but none seem to get the desired effect. In particular, I can never seem to get the router to respond to ARP requests on both ge-0/0/14.0 and ge-0/0/15.0 for the same IP. Any ideas on how I would be able to configure this network?