Have you already tried protecting you LDP sessions? This of course assumes that you have a redundant path available from your pe to the p routers.
mpls ldp session protection [vrf vpn-name] [for acl] [duration seconds]
You also need "mpls ldp discovery targeted-hello accept" on the other router.
Another possibility would be to use MPLS TE tunnels with FRR and run LDP over those tunnels (LDP over RSVP) so protect your LDP traffic. Although it would work, its a bit more complex solution but TE does offer the best recovery times for traffic.
Can you explain what kind of problem you have with LDP between the P and PE routers?
when I use auto-tunnel pri and back, even though I use POS sdh I still see some packet loss over MPLS VPN, and find out auto-tunnel Te for MPLS VPN converge is much slower than tunnel backup, but it is very tedious to manually configure backup tunnels.