Good solid "jack of all trades" folks, if they want to move up, need to do 1 of 2 things: (there may be others, these are the ones that jump out at me)
1) Specialize in at least one thing. This will make you an expert in one thing, while still being the person everyone goes to for other things as well. This will help advance to senior developer.
2) If you have a good grasp of the logistics of how pieces of a project fit together & the coordination necessary, another clear path to a more senior role is team lead where you do PM & part-time development. If you want to go higher than that, you're looking at high level project or product management. Actual development work will be minimal, but again with a jack of all trades background you will still provide valuable insight & guidance to those performing development work. And you can always look for extra opportunities to get your hands dirty back in to coding here & there.
In my experience, both personally and as a mentor to a number of "jack of all trades", (1) is good practical advice for jr generalists.
The OP appears to have significant experience already, and it does seem suboptimal to masquerade as a specialist in all job hunts, when that's not the real value you bring to the table.
Its leaning on the third clause of the full text of the quote: "jack of all trades, master of none, but oftentimes better than a master of one"... in other words, become a stronger specialist at one thing than most of the specialists in that area. That's great, and some of us can do it, but we're still not as strong as a specialist of our strength. It means you always interview as if you're a couple weight classes below where you actually are.
That's a practical compromise for a person starting out, but like the OP, with enough seniority, and the tremendous value that an experienced generalist provides, it feels bad to lean on that leg in all interview situations!
1) Specialize in at least one thing. This will make you an expert in one thing, while still being the person everyone goes to for other things as well. This will help advance to senior developer.
2) If you have a good grasp of the logistics of how pieces of a project fit together & the coordination necessary, another clear path to a more senior role is team lead where you do PM & part-time development. If you want to go higher than that, you're looking at high level project or product management. Actual development work will be minimal, but again with a jack of all trades background you will still provide valuable insight & guidance to those performing development work. And you can always look for extra opportunities to get your hands dirty back in to coding here & there.