Well its a bit hard (read superhumanly hard) to picture or fix the problem without seeing the network and knowing how you made it. I dont think you want to move your tweak nodes about, unless you are really on top of your game, as the tweak might do some collapsing the blend deforemer depends on due to the way it was created.
But lets take on step at the time, are we talking about a blendshaep that has the blend targets deleted or not deleted. (the beldshape works very differently in some cases when the nodes are deleted and when not because it only stores delta values wich can really shift when shufling things)
The biggest problem that i face here is that im working trough your understandings filters and the problem may in fact lie outside or likely on the finge your comprehension so it may be hard to get to the stuff, really. So i can just throw ideas around and hope you can solve based on my brainstorming. Do you understand how the history works? Or how the blendshape node works (no not just how you think it works but mathematically, since its probably the simplest animation node to understand of them all)?
All im trying to do is change de deformation order.
Deformation order is about understanding nodes, it sometimes magically works if you dont but in my experience thast more of a coincidence than anything else.