Just wanted to report back that YES the 4:55am bus does make it just in time! However I couldn't believe how long the check in lines were at that time!! We just had a bag to drop off and they did open an extra desk for the Edinburgh flight so we did get to jump the queue. This time we are going with hand luggage only.
I did see that in a few months the Friday flight does change times again so this is only temporary.
And
NO - I didn't sleep on the plane this time but I had the privilege to watch my other half snooze for the whole flight