If you make an NLA strip from any Action, any dupes of that strip will be affected by edits to the keyframes in the Action Editor/DopeSheet. The Action determines the “content” of the NLA strip in terms of keyframes.
To Edit the timing of different sections of an NLA strip, you’ll need to make your edits in the NLA Editor, using the tools there, which do not affect the base keyframes directly. For example, make an NLA strip of the entire Action. Then duplicate that, but set the start and end parameters of the duped strip so it covers only a portion of the original Action. Use the Scale parameter to slow this portion down or speed it up. This affects only this particular NLA strip. If you then make a dupe of the first strip (the entire Action) and “trim” it to the remainder of the Action, you can “butt-splice” the two edited strips in the NLA Editor so that the speed of the original Action changes from one portion to the next, but without affecting the keys of the original Action at all.
Obviously it’s a bit more complicated in actuality since you have to edit the NLA strips carefully to make sure your spliced edits flow together smoothly, but that’s the basic methodology. In some cases it might be better to blend the two edited strips over a few frames than use a butt-splice, but that’s all in the details (you know… where the devil lives )