Sorry for the delayed reponse, my life just went mental.
OK, firstly the experience of taking my bike on East Coast to Kings Cross was excellent. The guards van has 5 slots for bikes, with a metal slot on the floor to hold the wheels and a metal tube to velcro the bike to. The guards van gets locked and assuming you've booked a slot they check it in and out. You can book a slot online when you book your ticket, or if (like me) the tickets are already booked you can pop in to any mainline station and add the bike booking at no cost. Good service.
The morning route went pretty well and to be honest I found drivers to be careful and courteous. I'd avoid Bank at all costs - I got off and walked but it's very busy. The area around Aldgate also looked a bit scary, until I realised that the cycle crossing was there. I missed the entrance to the CS3, but once on it I thought that was a great route - a few joining side roads where you need to be sure drivers have seen you, but other than that very good and direct to Limehouse where Route 1 took me to Canary Wharf. The 6.4 miles took 1 hour 5 mins including navigating and maneuvering around Bank etc.
Coming back a friend advised me to try the Regents Canal. For a traffic-free route I'd definitely recommend it as long as you are prepared to be patient and give time to pedestrians and other cyclists. Especially going under the bridges. The 6.6 miles took 1 hour 20 mins but I had plenty of time and was quite happy to let walkers and other cyclists pass first.