Heathrow Express (even 1st class) is free between T1,2,3 and T4 if you are landside. Trains are at 15 min intervals. I understand the shuttle service is takes a while as well.

Your connection time is fine. With no luggage to check in (fingers crossed with Asiana), I have manage to do a self service check in 25-30 mins before the flight or a counter check 15-20 mins before the flight (not that I would be recommend or suggest this as a rule).