You may wish to visit the following FAA Chief Legal Counsel letters of interpretation on the subject, linked below. In the first, Asst. Chief Counsel Mark Bury refers t previous interpretations, and reiterates that while only time under Part 121 counts toward the requirement of 14 CFR 121.436, the FAA will look at previous experience for exceptions, particularly for time logged prior to 2013 when the current regulation was codified.
https://www.faa.gov/about/office_org...rpretation.pdf
That interpretation may not be helpful to your specific case, as your experience is not under a 121 carrier.
The next interpretation makes clear that other types of experience not under 121 are excluded from the experience requirement of 121.436.
https://www.faa.gov/about/office_org...rpretation.pdf
You can always petition the FAA for exception. Bear in mind that such efforts can be lengthy, and frequently unproductive.