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Oh, great illustration, and very interesting problem!
Is there some reason that you want to use Pattern Along Path? Like for example, you need to use the pattern more than once for just this image? Because if you just need it once, I think I would just flat out draw it, perhaps like you've made the pattern. Oooh, I think I understand now. The pattern needs to go all the way around the nucleus, and not just in the area where we see it in the illustration?
I'm embarrassed to say that I've forgotten so much science that I learned so long ago. I don't recall exactly what the endoplasmic reticulum does, and at first didn't realize it apparently, if I understand correctly, sort of encases or contains the nucleus. Or maybe it's new science? I really don't recall a smooth and rough version....
Anyway, so you've drawn something like a section of brick wall type of pattern? And then you need it to stretch around the circle (using pap), and then use Tweak tool. That sounds like a good plan, except that I'm with you. I'm not sure if the Tweak tool can be used on the result. I have to admit that Pattern Along Path has given me fits over the years I've been using Inkscape. I'll have to try to recreate what I understand that you're doing, or at least some representative sample and try it myself, before I can say for sure.
Of course someone else may come along with that knowledge already at hand. But that's fine -- I just like to learn!
If no one else has replied by the time I figure it out, I'll let you know what I learn

Edit
Well, I actually got a working example done pretty quickly, lol!
So yes, Tweak can be used on the result, but it won't have exactly the effect that I think you want. The Tweak tool only affects the original circle path, so that the individual rectangles get tweaked pretty much as a whole. So for example, instead of something like on the left, the rectangles will be more like on the right:

There might be a couple of ways to get around that. One is that you could tweak the rectangles before you apply them as the pattern. Based on my quick tests, I think you might need to make the pattern repeatable, meaning that each pattern will merge into the next pattern, without being obvious that it's a repeated pattern. That could get tricky.
So the other way I'm thinking is instead of several "rows of bricks" for the pattern, it would just be one row (tweaked before applying as pattern), but that you would have several concentric circles. I think this would appear more random after finished. You could tweak the rectangles before applying as pattern, and you could also tweak the result a little bit. And after you have however many concentric circles (looks like it would be maybe 5 or 6?) each of them tweaked separately, it would really look random. Or you could tweak the circles first, instead of afterwards, tweaking each circle a little differently.
A couple of tips with the Tweak tool. Certain modes have a tendency to create enourmous quantities of nodes, which can potentially bog down Inkscape. I didn't get anywhere near that point in my test, but I just wanted to mention it. Ironically, I had to create extra nodes in my 4 node rectangular path to get the right effect.
OH! Or I just thought of another way to approach the whole problem! This is assuming that I do understand the problem correctly

There would probably be more of a learning curve for this, though. But I think you could do a pretty good job using tiled clones, because there are settings for randomization. Edit menu > Clones > Tiled Clones. In Help menu > Tutorials > Tips and Tricks, there are instructions for making radially tiled clones. It sounds like there may be a few ways to accomplish it, but I've been fairly successful (not at this moment, but a week or so ago) making radially spaced clones, which leads me to think it might work. Hhhmmm....actually the tweaked rectangles would probably look very similar though, because the randomization settings affect placement, rotation, color, blur, and not the shape of the clone. You might be able to use 3 or 4 sets of radial clones, around the same center, using 3 or 4 different tweaked rectangles as originals. But by the time that you go to all that trouble, you might as well draw the whole thing from scratch. But it would be an interesting challenge to try

Anyway, let us know how it goes.

(And especially if I'm not understanding the problem correctly

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