Added note, I've re-read the bit about the OP's mobility. That being the case I would still stick with rail, but take a taxi from Euston to Paddington. (There are I believe now lifts down to the taxis at Euston which are underground - to the right hand side of the station concourse facing away from the platforms if I recall).

Those early Virgin trains don't tend to be busy (because of the outrageous fares, which the OP says are a consideration, but I think the timings here are down to "cheap, on time or accessible/comfortable, pick any two" to be honest), but you can reserve a seat to be sure, if you book in advance you may get a less outrageous fare, and I've never known HEx not have spare seats.

"Accessible taxis Yes
The route to the main taxi pick up point has steps, so anyone with mobility problems can use a taxi set down point reached via the lifts.

You can request assistance to and from the taxi rank can using the telephones at the top of the stairs and at the taxi set down point.

The main taxi rank is beneath the station and is reached via the lifts next to the main ticket office or the stairs by the entrance to the Underground."

Neil