There was a lot more green screen and CGI work used in TFA than is generally noticed but the characters are more compelling (even if the plot isn’t). And the integration is more subtle (most of the time).
Stylistically though you could take a good fanedit of the PT and ran TFA next they would sit quite well next together as 21st Century films.
The only real impediment would be the digital camera work on Ep2 and Ep3.
I agree.
(It would be nice though to get to see the PT with less CGI and digital colour-grading added to all the miniatures.)
Also shooting TFA on film did a lot in my opinion to help cover up a lot of the CGI (digital has improved a lot since the PT obviously, but I still think it helped). Just the fact that the actors, as well as what is actually practical, stood more out as real. This is why TPM works best for me (among the PT) despite the terrible writing and annoying characters, it just feels more real than AOTC and ROTS because of the way it was shot and the more obvious practical effects. TFA of course knocks all the PT films out of the park, despite being full of CGI (maybe even more than TPM?), because, as you said, the characters are much more compelling and likable.