Greetings @Wieland Handke!
The F-natural in bars 3 and 4 of the 1st and 2nd entry is very much intentional, even though it does generate a certain degree of instability not present in the original, fully tonal rendition of Mozart's own canon. In fact, I should thank you for highlighting the matter of accidentals, as the previous version did not, in fact, feature completely real transpositions of the theme. There were a handful of mistakes every 3rd bar, not contrapuntal, but harmonic and thematic, as the continuity and integrity of the transpositions was broken with leading tone and its minor 3rd/5th of a dominant chord being raised a semitone higher. All of that has now been corrected, so unless any more oversights of mine were to resurface, every single entry should now be a real transposition to the lower major 2nd of the main 18-bar-long subject.
I'm glad to learn that the current length of this canon would prevent it from seeming far too repetitive to the eyes of an educated listener. Indeed, I was worried it might end up sounding excessively mechanical despite the flowing timbre of legato strings, as monotony may distort even the most sophisticated of musical devices into pure pure noise after far too many identical, tiresome reiterations. It's a relief to know that to you it did not appear to be the case here, and I must thank you for your acute observations, for otherwise I might not have come to realize that the transpositions were not 100% exact.
I should also probably check @PeterthePapercomPoser's take on the Persichetti exercises, especially considering this canon on different scales you just mentioned. I'm anticipating a gold mine of modal/post-tonal contrapuntal solutions! Thank you for this recommendation as well.