Both your strings are incorrect. The <NOT> ειμι command eliminates hits which occur in the same verse as ειμι, rather than eliminating ειμι from the wildcard search.
So this string:
+διδωμι <OR> +ιστημι <OR> +τιθημι <OR> +φημι <OR> +δεικνυμι <OR> +ἵημι <OR> +ὄλλυμι <OR> +ῥήγνυμι @[verb] <NOT> ειμι
tells Accordance to find all these words except for +ῥήγνυμι when it is not in the same verse as ειμι.
had you used parentheses correctly as in
(+διδωμι <OR> +ιστημι <OR> +τιθημι <OR> +φημι <OR> +δεικνυμι <OR> +ἵημι <OR> +ὄλλυμι <OR> +ῥήγνυμι) <NOT> ειμι
(+διδωμι, +ιστημι, +τιθημι, +φημι, +δεικνυμι, +ἵημι, +ὄλλυμι, +ῥήγνυμι) @[verb] <NOT> ειμι
you would have eliminated all occurrences of these words where ειμι occurs in the same verse. (You cannot use the <OR> inside parentheses attached to @.)
So you must eliminate the ειμι with a minus sign connected to the @ expression thus:
(+διδωμι, +ιστημι, +τιθημι, +φημι, +δεικνυμι, +ἵημι, +ὄλλυμι, +ῥήγνυμι)@[verb]@-ειμι
However, your last method is much simpler, but again should not use <NOT> ειμι but rather the minus symbol:
Now each of these searches yields slightly different results, but I can compare them in a third tab using the Contents command thus:
[CONTENTS GNT28-T 2] <NOT> [CONTENTS GNT28-T] <AND> *+μι-ειμι
which yields a set of verses with the mi verbs highlighted for you to analyze and explore.
Sorry, I cannot go into why the results are different, but they probably result from the way that Accordance applies the search terms to the text in a slightly different order in each case.