> the Apollo flights never achieved escape velocity from the E-M system...
Yes, that was the plan from the beginning — the craft arrived at the right spot at the right time for capture into lunar orbit. Buzz and others have said they could feel the Moon before they saw it, as it was moving in and the craft was heading into its sphere of influence, distance being more significant than mass.
Except for ( I believe ) one midcourse correction Apollo 11 was in free fall right up to the LOI burn, and the was no way of feeling any sort of gravitational influence.
The only thing regarding the subjective experience that I’ve found so far is in FIRST ON THE MOON at the begin of Chapter 8, where it states the Bill Anders of Apollo 8 had very little awareness of the moon as they approached it. “Eventually Anders became aware that some great dark body was building up behind the spacecraft”.
Of course, such an impression might be felt subjectively as an impending influence, but it would be entirely based on the visual experience.