I'm not sure I'd want to try cycling through the tunnel, when it was opened in the mid 60s, the crossing took approximately 5 million vehicles a year, now it takes over 50 million a year.
I've only taken the crossing on a Landrover once, on the old FNRttC route to Southend. Even though Simon rang them multiple times (iirc, a few days before hand, on the day of the ride, as we left London, an hour or so before we arrived, half an hour before we arrived, and just before we arrived) they still took over an hour to get the first vehicle to the group. It then took two trailers loads, with some cyclists in the back of the Landrovers, and two or three mini-bus loads before we all got across. I think it was well over two hours to get us all across, and it was damned cold standing around waiting. Luckily the weather was merely chilly, and not raining, but clearly the bridge authorities couldn't give a rats arse about cyclists.
As far as I know no bikes got scratched, even though they were pretty tightly packed onto the trailer. The end of one of my Cateye bike lights fell off (it was a mistake to leave the lights on the bike), which made me swear a bit, but when I got to the services, someone had picked it up, and was wandering around asking if anyone knew who had lost it.
Possibly not so bad in daylight hours, and if there are only a few of you they can use a carrier on the back of a Landrover, so it should be appreciably quicker, but I don't think I'll make a habit of using that route.