Hi, first-time poster here. My thoughts during the first couple of weeks of this case were that he walked towards Barton Mills on foot and had an accident. I still consider this a likely explanation.
I would rule out AWOL (why start an AWOL escape with excessive drinking?!), military abduction (he was in civvies on a night out in a non-military town) and gay hook-ups (he was straight) but I have a fairly open mind otherwise. I consider abduction of a sexual (rather than military) nature to be a possibility. My thoughts are as follows:
He sat down in the Hughes doorway (perhaps to bide time until his friends left Flex but perhaps not) and unintentionally fell asleep; when he awoke, he decided to make his own way home.
He then walked via the Horseshoe out of Bury. The fact that the Horseshoe is the final CCTV footage has given it unnecessary prominence. The police haven't said he couldn't have left by foot and I believe walking along Short Brackland is still a real possibility.
In a drunken state of mind he walked in the wrong direction (probably along the A1101) in the general Barton Mills/Mildenhall direction.
Given that he's a healthy guy, he probably walked at 3mph and the pings, which I believe suggest he left the Bury phone mast at around 4.30, would support this. (Occam's razor would suggest that he and his phone were still together - I think it's unlikely they got lost in different directions!)
Between 4.30 and 5.00-ish he was outside the scope of both the Bury or Barton Mills masts - if either of these masts had a range of 3-5 miles, the distance walked between these times may only be 1-3 miles.
If he had sobered up sufficiently when he realised he'd made a wrong turn, he may have decided to continue to the nearest town, i.e. Mildenhall, rather than walk the 15+ miles to Honington. This would have made it easier to catch a taxi or bus back to base.
Corrie may have changed his route to avoid the footpath-less and verge-less A1101 from either Lackford or Icklingham onwards. Assuming he had his phone and he had sobered up a bit by now, he would be able to check his map app and find an alternative route. Many of the footpaths near Lackford are near lakes and the main footpath from Icklingham to Barton Mills is by the River Lark and grazed by intimidating cattle.
Corrie could have slipped into a lake or river, which would explain his disappearance and the timings of the mobile phone pings.