I added router 5 in my topology and tried configuring it as both an ebgp and ibgp neighbor to R4 in both configurations it received routes advertised by R1. However, you would need assistance from your mpls provider. Your provider is saying that they have the configuration in place and therefore it shouldn't be blocking prefixes that have the same as-path as the mpls cloud then why is it not reaching site B router?
Please let me know if there is something I am missing about your topology.
Did you try debugging bgp updates and trigger inbound route refresh?
R5 bgp routes as an ebgp neighbor:
R5#sh ip bgp
BGP table version is 6, local router ID is 40.40.40.5
Status codes: s suppressed, d damped, h history, * valid, > best, i - internal,
r RIB-failure, S Stale, m multipath, b backup-path, x best-external, f RT-Filter
Origin codes: i - IGP, e - EGP, ? - incomplete
Network Next Hop Metric LocPrf Weight Path
*> 1.1.1.1/32 40.40.40.4 0 100 300 200 100 i
*> 2.2.2.2/32 40.40.40.4 0 100 300 200 100 i
*> 3.3.3.3/32 40.40.40.4 0 100 300 200 100 i
*> 4.4.4.4/32 40.40.40.4 0 100 300 200 100 i
*> 5.5.5.5/32 40.40.40.4 0 100 300 200 100 i
R5#ping 1.1.1.1
Type escape sequence to abort.
Sending 5, 100-byte ICMP Echos to 1.1.1.1, timeout is 2 seconds:
.....
Success rate is 0 percent (0/5)
R5 bgp routes as an ibgp neighbor:
R5#sh ip bgp
BGP table version is 1, local router ID is 40.40.40.5
Status codes: s suppressed, d damped, h history, * valid, > best, i - internal,
r RIB-failure, S Stale, m multipath, b backup-path, x best-external, f RT-Filter
Origin codes: i - IGP, e - EGP, ? - incomplete
Network Next Hop Metric LocPrf Weight Path
* i1.1.1.1/32 30.30.30.3 0 100 0 300 200 100 i
* i2.2.2.2/32 30.30.30.3 0 100 0 300 200 100 i
* i3.3.3.3/32 30.30.30.3 0 100 0 300 200 100 i
* i4.4.4.4/32 30.30.30.3 0 100 0 300 200 100 i
* i5.5.5.5/32 30.30.30.3 0 100 0 300 200 100 i
