What you're trying to do is not good practice in network design. You shouldn't have overlapping subnets within the same contiguous network.
That aside, filthy hacks are a hobby of mine, so I'll make some (ugly) suggestions as to how this might work.
So, the first one that comes to mind (if your hosts support it):
1. Configure the SRX interface that points towards the host as 192.168.1.0/31 and the host itself as 192.168.1.1/31 (255.255.255.254) with a default gateway of 1.0.
2. At the other end, make the SRX interface 192.168.1.3/31 with the host as 192.168.1.2/31 with a default gateway of 1.3.
3. Re-distribute into OSPF and you're done.
I suspect you probably can't reconfigure the hosts though, or you probably wouldn't be attempting this. So, filthy hack no.2:
1. Firstly, redistributing the subnets into OSPF is *not* going to work. Create a static host route (/32) on each SRX for the far-side host and give it the next-hop of your tunnel interface (assuming route-based VPN here. Another hobby of mine is hating on policy-based VPNs)
2. Enable proxy-arp on the host-facing SRX interface for just the address of the far-side node and you're done. This should draw traffic towards the SRX as it responds to ARPs on behalf of the far-side device and the static host-route should ensure forwarding.
I'm sure there's a third hack in there somewhere involving routing-instances and route-leaking and proxy-arp, but I'll leave that as an exercise for you to explore if you don't get anywhere with the above two options.
Hope this helps
If only J-Net had a "Mark as Filthy Hack" button....