I can absolutely sympathize with you. I'll give you my best example as a method of comparison.
I work as a 1099 contractor as well, albeit on temporary contracts, and there was (initially) roughly a 50% difference in amount that I billed the company I work for and what they billed the customer. (If I billed $50, they billed $100)In the first year, I had NO IDEA what kind of value the company was receiving on my behalf.
Fast forward to year two. I'm now being personally requested by our customers. Company offers to pay me more in lieu of taking on more responsibility. Margin drops to about 40%, I keep 60%. I take the offer. I begin to realize my monetary value, AND my capacity.
Fast forward to year 3. I realize that I'm going to be doing this more permanently. I begin voluntarily taking on nearly all of the upfront tasks/responsibilities while maintaining the same contract wage. Company is no longer dealing with customer first hand, but barriers to entry prevent me from replacing the company personally. Eventually, the company does nothing but make money every day I work. I only need them to provide the leads. 3 months later I tell the company I contract to that I want to renegotiate the contract. I tell them I want 85% of the gross contract amount, they will maintain 15% of the contract. They fight back, offering a 30/70 split.
At this point I realize I have the "FU Position" on my side and stand my ground. Either they give me 85% of the contract award rate and settle with keeping 15%, or they lose their best/most valuable contractor and make NO money on my behalf ever again.
They have no option but to settle and accept. I believe they value the fact that I am a guaranteed income generator for them. When I'm on the job, they make money with NO hassle.
I do wonder if there will come a time when I am replaced, but I also know that certain aspects of my job/capacity are irreplaceable short term and thus require long term planning. I.e, I will see it coming in advance. Until then, I'm preparing my FI for future "FU status" negotiations.