I also start out the way you do, cutting things up (usually in phrases in my case) across the whole track, as close as I can get to a breaking put that will be the same across all takes, even if it might not be the best for any given take, including extra space at the end of phrases before big breaks to make sure the longest phrase ending is kept, which may mean extraneous noises in other takes.
While I’m comping, and selecting individual sections for each part, sometimes having to cut things up more finely to deal with issues, I may be adjusting the clip boundaries based on the clips I select, and that may make issues in other areas for phrase boundaries, but I don’t worry about that, for now.
Once I’ve got an entire song section (e.g. verse, pre-chorus, chorus, etc.) comped, I move the selected clips up to another track with the same processing on it (I’m usually using some processing in the course of doing my comping to help me review the parts, for example an automatic tuning plugin to help me both minimize any minor tuning considerations, since I’ll be manually tuning later, and exacerbate any more significant considerations, since that may change which takes I pick for some parts). If I need to comp doubles from the same pool of takes (which I pretty much always do for background vocals and occasionally for parts of lead vocals), I’ll then comp the next set from that same section. If not, I just mute the now selected parts in the just-comped song section in the original track so I won’t hear those when playing back. (I might note that I usually comp from the end of the song forward, partly because I want to pick take components that flow together well, so I’m listening not only to the takes I’m selecting at the time, but how they flow into whatever is immediately after them.)
I’ll typically finish comping the entire song for the part(s) I’m working on from a given pool of takes before doing any editing on the comped track(s). Once I’ve finished that, I disable the original track with the (now unused) takes and move it to a folder with any accumulated changes (in case I need to change my mind much later in the production process – e.g. I’ve sometimes needed to do this when comping decisions have ended up making for artifacts in later stages).
Now I go to the track with the comped part and do fade/crossfade editing, any volume adjustments, clip envelopes, possibly restoration processing (e.g. if there are clicks, I might use RX to deal with that), etc. I’ll be adjusting clip boundaries during this process to optimize it for the selected clips, and the transition points may be quite different from what they were in the original set of takes. Once I’ve done all that editing, I’ll generally bounce the clips into song sections (after having made a backup of the track with the edits intact to put in my old tracks folder “just in case…”), which are what I tend to like to use for subsequent work (e.g. using VocAlign to tighten background vocals and/or doubles against the lead vocal).
I guess the bottom line with respect to the original question/issue is that I don’t do any of the heavy lifting on fine clip boundary changes while working in the track with the pool of takes. Rather I wait to do that on a separate track, where I can optimize any changes for the clips in the comp. And, of course, if I need to comp more from the same pool of takes, I can adjust boundaries for what remains as needed while doing the further comps and again do the heavy lifting later.