It make no difference physically alternating, it is a mental pursuit which finger you start on...if you want to make it one.
Physically your finger follow each other when alternating so it makes no difference if the forefinger follows the middle because the will be following the forefinger, and as surely as you play you can call it forefinger following the middle or middle following the forefinger....it is just alternating.
What you experience in the un-natural part is the influence of beats and strong beats because your forefinger feels the strong beat at the start, and in simple time signatures as a rule you will find a strong beat at the start of a bar that your forefinger will go to.
Now this is not a problem because lots of music has this feel. but if you move to compound time signatures, or music where the string beat is not in fours, the tendency is to "trip" over the fingers or "rake" the strings or double play with the forefinger.
Answer is start with either and practice to play starting with either. What ever you can play no practice it starting with the "wrong finger". Once your brain gets used to it ( learns that it does not matter) the problem will disappear.
Thinks on this situation, you play music and the beat changes around then so will your dominant finger, if you just play the music and use the next finger available regardless of the strong beat then it will not matter what finger you start or finish on. The fact is you are creating a condition where you play the music for the musics sake not any techniques sake.
If you know fretting hand scales shapes for major scales that start on the middle finger the play this one finger one fret.
C-D-E-F-G-A-B-C-D-E-F
As you will see you play the scale starting on the C with the whatever plucking finger and finish the standard 8 note scale on the alternative one.
But because you are going through to extend to the 11th (F) you effectively start the second C with a different finger to the Root so arrive at the 11th on the same finger as the Root.
Now that will confuse your brain for a moment if you work in 4s divided into 2s ( two fingers to handle the task) when you try to go back down those notes to the root, because you are not working with a dominant fingering.
So you will see that when you go up the 11 note scale you will finish on the same finger you started call it F1, and when you come back down ( alternating the whole way, no starting new) you will end up on the opposite finger to the start Root F1 and will now be on F2.
When you go back up again starting with F2 you will arrive at the 11th with the same F2, and when you go back to the Root you will be on F1....and so repeat and repeat till you can do it without thinking just playing...then move it around to different positions on the neck as before.
You can then do minor shapes to the 11th with the same ideas, but as the minor shape require a slight fretting hand change to acheive the one finger one fret idea, the challange is slightly more, because the movement of the hand may want you to consider that as more than it is.
So to re-capp treat any scale over two octaves and play any 11 notes ( remember 11 note up and down alternating is 21 notes. If you replay the 11th note that makes it 22 and your are back to dividing fours into twos) so it shoUld play
C-D-E-F-G-A-B-C-D-E-F-E-D-C-B-A-G-F-E-D-C
for C major starting on the C root.
Have fun and read this a few times to get the idea of what you need to do, its not hard to do just hard to explain hence the long post. In reality this exercise takes about a couple of minutes to explain and demonstrate, also look out different forms of music that will challenge your timing...Latin for example, or reggae.
