As you've observed a "combine" of tagged PDFs puts the assorted PDF's Structure Tree (the "tags") through the mix-master blender. Don't use "combine".
RE: Acrobat's "auto tag" feature -- That's sort of ok for a single, simple document. The output still needs manual remediation. You are not working in "simple" so don't waste life-minutes walking that path.
Upfront, identify the desired content sequence (pdf-1, pdf-23, pdf-591, pdf-6, etc.
Open the first PDF. Use an Insert operation to place the second PDF after the last page of the first PDF.
The second PDF's Structure Tree will be at the bottom of the Open PDF. Do an immediate Save As. Use a prefix or suffix with the file name and increment it as you'll Save As frequently.
(There's no "undo" for the manual editing you have to do to the Structure Tree. Without a good Save As routine you can/will lose hours and hours of work faster than you can blink your eyes.)
Remediate the Structure Tree of the "new" PDF (pdf-1, pdf-23). Save As frequently.
With this first round of remediation done repeat the process. Insert the third PDF at the end of pdf-1_23. Remediate the Structure Tree. Save As often.
(n.b., to optimize success and timely completion of manual remediation it is most useful to be well versed in Clause 14 of the PDF ISO Standard.)
For the scenario you've describe what may be functional "programmatic" tool is Netcentric's 'CommonLook". Expensive with a serious learning curve.
More an "enterprise" (with available $$ in the budget) tool rather than something an small business or individual would use.
Thanks, Dave. We are exploring the possibility of CommonLook, but have not yet decided. Do you think that Acrobat 11 as opposed to 10 would be an improvement?
No, not really. For this particular activity there's no difference with different versions.