Maybe something like the VSS if it seems fine going backwards? Have you really tried booting it backwards to see if it totally fine when reversing?

Also you mention it was low on fuel so I would think about looking at changing the fuel filter (relatively cheap about £12 for Ford although since I last bought one might be about £32 now lol). Blocked cat would also caused above issues if running lean but strange as to why it won't do it when reversing...

Does it rev clean when in neutral?