I'm being told to sit on thisThis question is more problematic than you think. You should consider resigning and getting a new job.
Insubordination will not only put you at risk for losing your job on an involuntary basis, but in a precarious legal position should you be fired. (Your company will have the ability to deny you unemployment, and/or provide a reasonable professional reference.)
That being said, the way to handle your situation is to "skip-level" your boss. Most established companies provide for this (potentially via the HR function). The purpose of a skip-level is to raise issues internally that are important to the business but may be bottlenecked by a conflict of interest in middle-management.
This is a situation that needs to be handled with discretion. You don't want to trigger an emotional reaction from anyone about this--stay away from ad-libbing stuff like "I think our engineers are lazy in the wrong way"--you simply want to resolve a remediable inefficiency.
The key considerations for you are (1) establishing credibility, if its not already evident to your 1-over-1 manager; (2) being forthright with the risks (and fairly treat your immediate manager's stated position/s); and (3) finding a way to implement a decision without making your boss look "lazy in the wrong way" {etc}.
The question to you is really about the upsides to taking a pro-active approach?
The standard for that upside should be reasonably high. Can you deliver results to both your immediate boss and your 1-over-1 boss by doing this? If so, and if this will decrease any disfunction/toxicity (rather than trigger it), that is more persuasive.
If this is just going to inflame a bad situation, then again you may want to just look elsewhere before sinking more energy into a dead-end rabbit hole.
The downsides to doing a skip-level are mitigated by the discretion of your HR and 1-over-1 manager if this is simply declined. The messier edge case is where they decide to implement your fix, but something goes wrong technically or in the political implementation that damages your own reputation (for showing good judgement).
The bigger picture question: if the culture is "rotten", what are the odds that your skip-level is an equally un-satisfactory decisionmaker?
A "cowboy" implementation (with no approval) is unlikely to trigger a cultural renaissance you have multiple layers of bad management. It is possible, but remember someone up above you thinks those guys above you are "decent-enough". So you're initiative would have to overcome essentially 3 bad layers of managemnet--that is alot of inertia.