There are many extra little variances depending on the type of guitar and the tech involved.
What type of guitar are you using?
Until then I'll give a list of some extras to consider, especially if you're changing string gagues.
On an Electric guitar
- Adjust the Intonation
You need to check that you get the same note at the 12th fret and on an open string. If they're out of tune then you need to adjust the intonation so that they're in tune.
On a floating bridge(ibanez)
- Once tuned, adjust the bridge spring tension to align the bridge, retune and repeat until you have nightmares
- roughly tune with the main pegs, lock, then use the micro-tuners for fine tuning.
If you have a floating bridge let me know, because they deserve a long answer in themselves!!!
I found a video for acoustic. I think you pretty much have all the basic steps for that, but I may be wrong!
I've always believed this would help preserve stuff like neck tension, action, and all the other fine details. Does this make any sense?
I have it from a luthiers shop that the guitar neck is extremely strong. Before you get to any kind of tension that would do damage you'd more likely snap the tuning pegs off the head!
As far as action goes, I don't think that has a massive effect when changing strings because action is to do with how high the strings are from the body. I guess heavier gague strings will be slightly closer to the neck which may cause a fret buzz, but apart from that I've never had an issue that I can remember.
Is there a widely accepted method for replacing the guitar strings?
Yes, and you've pretty much described it :)
Hope that helps!