What do you consider "influencer marketing"? Consumers with lots of friends or bloggers, health professionals and other ambassador types? Each would be approached differently.
"am I right to believe influencer relationships themselves are possibly my most valuable asset (brand + retail distribution channels in a close second)?"
No. Your most valuable asset depends on your core competency or competitive advantage. It could be operational, financial, intellectual, hr or marketing-based.
Based on the brief info you've provided, let's assume it's marketing based. You would then need to look at which of the four basic "p's" - product, price, distribution and promotion you have a clear competitive advantage in. If you have pre-existing relationships with retail/salons then it might be distribution. If you have a product that addresses a need that is currently unfulfilled, it might be the product itself. If you have a unique pricing strategy or positioning, that might be it. But if you don't have a clear advantage on any of the above, then yes, it's promotion, which includes your influencer marketing strategy and everything else you do to create awareness, trial and sales.
I find it's instrumental to have a precise understanding of your competitive landscape (especially in such a crowded space) so that you can get a clear understanding of how to best position your product, which will then dictate the 4Ps.