I think that you will always have to deal with some amount of B.S. as long as you're spending other people's money. That's unavoidable.
The B.S. is amplified however when you're at a big institution. There's a lot more red-tape even if you have private financiers.
One way would be to yes, keep burn low. The idea there right would be that you're asking for less money, you're lowering expectations of those giving you money. If someone gives you $1000 they're going to micromanage you a lot less on how that money is used versus if they give you $10,000, $100,000, etc. The other idea is that if you have less stakeholders there's also less back and forth that needs to be maintained with them.
My idea would be that you'd avoid the incentive-skewing over the long term by doing some research that can be converted into revenue generators to cover the base costs of running a lab. Reinvesting profits into traditional finance products to get a yield on the lab's money. Even running a small scale cryptocurrency mining operation as a single part of revenue generation. If you combine this with low-overhead by being smart about what would typically be big ticket purchases that only the most well funded of labs can afford and finding people with a like mind who are willing to take a liveable(but smaller wage) to work in a more open environment then it should be sustainable. For me in particular I can balance research time with programming consulting time and make 80% of what I would make in Biology/BINF or at an academic institution without breaking a sweat.
Like I mentioned before about grant skimming by institutions.. If you're a PI at a state lab or university they will take a "generous" portion of your grant as soon as it arrives. I'm specifically thinking of one guy I know who recently had HALF of his grant taken for facility rental and upkeep. It was a large grant mind you. In another case a friend who had finished his postdoc and was a first time PI landed his first grant. As soon as it was in the lab managers tried to say "awesome, now we can pay your salary out of the grant" He had to play hardball with HR to state that his salary was guaranteed and not to be paid out of grant money intended for his research. Now I can understand why this happens. It's not free to run a research enterprise, and it's not particularly cheap when you're buying equipment at MSRP. Research equipment in the second hand market before it goes to professional refurbishers is literally cents on the dollar. It's so specialized, there's a small market for it, and big players are not buying this stuff because of the inherent risk! In my experience though the defect rate is so absurdly low that it's not an actual risk buying this equipment. But it's not something an institution with a multi-million dollar grant to setup a research center/core is going to waste their time on.
As for specifics of what I'm aiming to do. I intentionally picked a research area I'm going to delve into that has low costs. An operation like I'm talking about in my OP would not be feasible for high energy physics or high cost sequencing projects. I'm focusing on photobioreactor design and algae cultivation yields for animal feed, biodiesel refining, etc.
For that I need CO2 incubators, centrifuges, a 3d printer, algae samples, a sample freezer, turbidimeters, photospectrometers, pH meters, and then a revolving supply of plant fertilizers, CO2, and Nitrogen. But before I get deep into actual PBR design and cultivation techniques I'm going to work on computational models for PBR design, algae growth rates, and PBR monitoring software for data collection.