I am winding a fluffy product with final specifications on Outside Diameter and Mass. The basis weight and caliper (thickness) ranges are quite wide compared to the final product desired OD and mass. The density (basis weight/thickness) of the media definitely can change within the supply roll of media (due to the manufacturers process). You can see that I am winding blindly to an OD and praying the mass meets the final specification. If I have communicated the problem or question properly, I can provide more information.
While the question is slightly difficult to pose, the explanation is even more involved and requires a bit of winding science. Here is the executive summary.
1) Winding is a 1 knob 'process'. Once you pick one thing, everything else is determined.
2) Picking two things simultaneously, such as roll diameter and roll length, is overconstrained.
3) This means the result will be the following possibilities given that variability of manufacturing will occur.
a. if the specs for diameter and length are too tight and/or not centered on the process, the result will be out-of spec product
b. if the specs for diameter and length are too loose, the wound roll may vary from unacceptably loose to unacceptably tight
I had a technician once who summarized the situation more succinctly: "if it ain't there, it ain't there." What he meant is that you can wind adequately tight rolls when manufacturing gage/weight drifts.
So you see that this is not a winding problem per se, because these constraints exist no matter what type of winder you have and what the winder settings are. These constraints are built into physics, the fabric of the universe if you will. The winder can not help the situation. All the winder can do is to make things worse by not holding settings or having some limitations of range of settings.
There is almost nothing on this in the general literature. I have written on this for the tissue industry where the situation is almost identical and where product compressibility allows a bit of leeway for manufacturing variability. Here we turn the product/process specification into a design science connecting roll diameter/length and roll firmness (corresponding to mass or tightness in your case). This is attached. I have more theoretical discussions in my Web101 CD and also in my thesis, but I am not sure how helpful that would be.
A final admonition to those writing specs for soft products: just because you have achieved diameter target and just because you have achieved a tightness target does not mean you can achieve them simultaneously or achieve them reliably.