Am I correct in thinking that, if I am the original and sole author (and the code was not produced as a work for hire) of code contributed to an open-source project with a given license, I retain the rights to use that code however I please (including in violation of that license) and contribute it to projects with other, perhaps incompatible licenses (which presumably would result in the code being multi-licensed)?
If you are the sole rightsholder in the code you are contributing, and you do not also complete a Copyright Licensing Agreement (CLA) or a Copyright Transfer Agreement (CTA), then the position is as described in this answer: you retain the rights to your contribution, and may still do with it as you wish. There are potential complexities if you later try to do something that is sufficiently similar to the project to which you contributed, and that contribution was made under a copyleft licence, because you presumably will have studied that larger project carefully in order to made your contribution. Thus, any future reimplementation you do might reasonably be suspected to be a derivative work of that larger project, and (if it were) thus also subject to those copyleft rules. This may affect the choice of licence for that future project.
If, however, you've made your contribution and completed a CTA, then you are no longer the rightsholder, and have no more rights to your contribution than any other member of the public.
If you've made your contribution under a CLA, the position will depend on what, exactly, the CLA commits you to with respect to reuse of the code. Were this the case, we could not comment further without seeing the CLA in question.