I would respectfully point out that your post has a few "red flags" for what we in the business call "crankery."
My...paper is being rejected..without undergoing peer review. However, every rejection explicitly states that there is no technical error in my line of reasoning and so far none have questioned the relevance and novelty of my work.
This does not make sense, how could the editor "explicitly state" that there is no technical error if the paper has not been peer reviewed? How would the editor know? Moreover, even published papers don't get an "imprimatur" that the work is correct; rather, the work is judged sound enough to be published.
It is more likely that the editor said something like "this desk rejection does not necessarily imply that your work is not technically sound" -- as mentioned in the comments, the paper has not been peer reviewed, so no one has bothered to check if the work is correct or not.
From my limited perspective it appears that my paper is being judged subjectively for its implications to physics... I am an outsider to the academic field
I'm not sure quite what you mean here. Hopefully you are not alleging that your paper is so groundbreaking that the physics community has formed a conspiracy against you. Rather, I assume you mean that you are not getting a "fair shake" since your conclusions seem so surprising. Such things can happen, especially since you are unaffiliated with a research institution. We like to tell the story of Prof. Zhang, where the system worked as it should. However, it's true that you may need to take some extra steps to get people to take you seriously.
After five rejections from reputed physics journals...
After five rejections, it does seem like something is wrong. This could be something minor, like selecting a more appropriate journal. Or it could be something major, like the entire idea being "crankery." Personally, I would rather know -- if I am wasting my time, I would rather someone tell me so that I can pursue other activities instead.
So: I would recommend that you buy a few hours of a graduate student's time (preferably one who works in your field). In exchange for, say, $200, they should be willing to spend a few hours giving you a peer-review. If the work is mostly good, they may have advice on selecting a journal and writing it up. If the work is mostly bad, they may be able to point out some technical flaws. But in the latter case, I would recommend abandoning the effort entirely -- I've seen before that there is often a disconnect where the expert says "this is totally wrong; for example, your electron mass is an order of magnitude too high" and the non-expert hears "if I can solve the electron mass problem, we're good!" This communications breakdown can lead to much wasted time.