This is not a complete answer, but more an idea on how it might work. It is, however, way to long for a comment.
The idea is to patch the \include command that it internally uses pdfpages to input the parts that are not mentioned in \includeonly from some existing PDF from a previous complete build. Some clever arithmetic might be necessary to calculate the page numbers, but in principle this could work.
A big issue might be hyperrefs. All parts are compiled with the same .aux files, so labels and page anchors should be consistent. However, they are lost when embedding PDFs with \includepdf. Nevertheless, in conjuction with (2) pax it might be possible to fix this. From the pdfpages documentation:
Links and other interactive features of PDF documents When including pages of a PDF only the so called content stream of these pages is copied but no links. Up to now there are no TeX-engines (pdfTeX, XeTeX, ...) available that can copy links or other interactive features of a PDF document, too. Thus, all kinds of links1 will get lost during inclusion. (Using \includepdf, \includegraphics, or other low-level commands.)
However, there’s a gleam of hope. Some links may be extracted and later reinserted by a package called pax which can be downloaded from CTAN. Have a look at it!
pax is a combination of a Java tool to extract link information from the PDF you intend to embed and a package that reads in this information to restore the links into embedded PDF. It is still considered as experimental and I have not tried it. However, it is written by Heiko Oberdiek, so I would be optimistic that it works.
To conclude: Given some decent TeX skills, I think that your idea is achievable. However, given the complexity and involved tool chain, I doubt that in the end this is would be a big time saver. If compilation time is the issue, I suggest to consult How to speed up LaTeX compilation with several TikZ pictures? for other optimization strategies.