Hi David.
Welcome to JustinGuitar and the Community. For structured learning with a supportive network of fellow students you have found a wonderful musical home.
Selective quoting …
You are truly in your infancy and, rightfully, should be nowhere near the F barre chord after such a short time.
… I don’t seem to have too much trouble making the dreaded “F” chord … when I move around the neck into different positions, I have trouble applying the same technique …
That you are making the F chord work is an impressive feat. That said, I recommend you stop pushing the bare chord so rapidly. If you can play F major then you have a full complement of diatonic chords in the key of C and have the opportunity to play thousands upon thousands of songs (if transposed to that key) and thousands upon thousands of other songs that do not rely upon a full diatonic set of chords.
Using just the most common guitar keys, you have the following chords available to you.
There are gaps in several of those keys yet none of the gaps would be filled by E-shape major barre chords. All of the gaps are minor chords. These are most readily played on one of two barre chord shapes that you have not yet learned and do not need to consider learning just yet.
… what kind of exercises can I do to develop stronger muscle memory …
Learn songs, learn songs, learn songs.
… I don’t have problems playing open chords or switching between them …
In that case apply your new skills. Play songs, learn songs, lots and lots of them.
Go here for dozens of song lessons and use the filter tools if that helps you narrow things down.
… I work regularly on finger exercises …
Good.
… and diatonic scales …
I recommend you remove scale practice from your practice time and spend your time on other foundation skills and techniques and songs. Guitar is unlike piano inasmuch as you do not need to learn scales as a foundation. Scales come along later on and the recommendation from Justin is to only learn one scale, one pattern and make music from it before even considering learning another pattern or another scale.
… I try to be very regimented in practice …
That is to the good.
… concentrating on learning the notes of the fretboard …
That is a good long term goal but need not be a central focus of your practice time at this early stage. If you are going to learn note names on the fretboard early on, concentrate on the open strings and up to fret 3 with the natural note names. These will coincide with learning the open position C major scale.
… and applying my understanding of music theory to get in the habit of reading music for guitar.
Having music theory knowledge is great. As is the ability to read standard music notation. Unless you are going to learn and play classical guitar then you will encounter very few occasions in which you will find or need to use standard notation for guitar music. It will be either TAB or chord charts. Justin has a great course of Practical music theory which is specifically aimed at music knowledge relevant to guitar.
… I think it is likely the action on my guitar is too high
That can make the playing more difficult, less enjoyable and less musical (having to press the strings further can make notes sound sharp).