Your standards aren't too high but I think you must realise that this is a cultural problem with little hope of changing. Even if the push comes from the CTO, it will take years for change to happen, it will require new hires and bringing new blood into the engineering leadership.
If you do want to take the challenge (which I strongly discourage you from) you'd need to collect data to build your case, quantify the time and human cost from issue/jira to code landing in prod to number of incidents/bugs. The instrumentation to do this will be a fairly chunky piece of devops work. Frame the data in light of your competitor's ability to iterate their products and so on. When it's collected and presented it can be quite compelling and people will listen.
It's only at this point you'll be able to present the problem to management in way that they understand. You know and I know that this is a cultural problem first, then a process problem and lastly a technology problem. The amount of work to effect this kind of organisational change, even in a small engineering company is immense. I don't know your motivations are for staying, if it's the domain or the money but if this something that bothers you then this is the best piece of advice I can give you:
> this is a cultural problem with little hope of changing
I disagree. Most existing teams with good processes started out decades ago without them, and improved incrementally from where they started. Team culture can absolutely be changed, but it takes a lot of time (and requires cooperation from seniors and managers).
If you do want to take the challenge (which I strongly discourage you from) you'd need to collect data to build your case, quantify the time and human cost from issue/jira to code landing in prod to number of incidents/bugs. The instrumentation to do this will be a fairly chunky piece of devops work. Frame the data in light of your competitor's ability to iterate their products and so on. When it's collected and presented it can be quite compelling and people will listen.
It's only at this point you'll be able to present the problem to management in way that they understand. You know and I know that this is a cultural problem first, then a process problem and lastly a technology problem. The amount of work to effect this kind of organisational change, even in a small engineering company is immense. I don't know your motivations are for staying, if it's the domain or the money but if this something that bothers you then this is the best piece of advice I can give you:
Run, head for the hills, and don't look back.