Originally Posted by JohnBurke

Established: you are not working for a US carrier.

When flying in the United States, yes, you must abide by the regulations established under Title 14 of the Code of Federal Regulations. That has nothing to do with your eligibility to fly for a US carrier, or your eligibility to obtain an airline transport pilot certificate.

Whereas you're not operating as pilot in command under 91K, 121, or 135, as previously discussed, your experience does not meet the requirement of 14 CFR 121.436(a)(3).

Previously you stated that you believe your "Operations Specifications" state that your work "falls under 14 CFR." That is incorrect. I don't know what "Operations Specifications" are assigned to you, but as you've established you're not working for a US certificate holder (charter, airline, or fractional), you don't have US Operations Specifications.

What you've cited is a requirement by your regulatory authority that you will abide by US regulations when operating in the United States. This applies regardless of who you are. If you fly in the USA, you'll abide US regulations. This is a blanket requirement as it is with any ICAO operation; you must still observe the regulation and legal requirement of the country in which you are flying.

If you wish to fly for a US carrier, you'll also need to meet the experience requirements applicable to that carrier. In the case of an airline (121) operator, you'll need to have the requisite experience to upgrade, and as 121.436(a)(3) spells out, you'll need a thousand hours of experience under 91K, 121, or 135 before you can upgrade.

Presently your situation does not meet that requirement.