First of all, this is a very nice description of the message flow! One question remains for me: in Step 7 of the message flow from the AFW to the IS you explained that the IS URL is retrieved from the SLD. However, in Fig. 1 you illustrated that the ...
It hangs in the outbound Adapter - which one are you using? I guess the IDoc outbound adapter? IF so, go to transaction SM58 and restart them there. Even better: plan a job to do that regularly (RSARFCEX, restart of tRFCs).