> battled with the knowledge that life has no intrinsic meaning
Yes, it doesn't. But we can choose our own adventure, create our own meaning. I organize a summer camp for ~50 people. Is there any objective value to it? No - we'll all die and no one will remember. But I derive plenty of subjective value, as do the other participants. Is it worth it to do this? Objectively, no. For me subjectively, yes.
Have you read Man's Search for Meaning by Viktor Frankl?
By ill-posed I simply mean it assumes something under the hood. Like when someone says "how do you catch X criminals" without first establishing that X is a crime. It's kind of a trick of language.
I do not like your parallel. The question about the meaning of life can also have the answer "there is no". It does not assume anything under the hood.
Meaning to me for example is conquering my existential problems (anxiety, depression), pushing past boundaries and percieved limits in life, seeking love and obtaining goals. These examples provide substantial meaning for me, where I'm currently at in this point of time. So meaning to some degree are what you value, subjectively speaking.
Just ask yourself - what does it mean that the "meaning" of X is Y? In the "meaning" sense that this thread is about.
The very fact that anything is happening, that there's something rather than nothing can be all absorbing. The "meaning" as people usually put it is typically a case of mis-wanting, trying to fit the reality to the language of thought, rather than the other way around, and a lack of focus on the present. In particular the religious concepts of heaven and hell are the most prominent members of this category (throughout the written history, and perhaps much earlier).
I gave up on any notions of mysticism - religion, higher meaning and all that and instead just accepted causality is all there is. Things happen because they're the only logical thing that could happen given the conditions. Think of it as taking Markov to a broader sense.
You know what's so great about that, that relieves me so much? That there's no plan for me. No one is going to fix my issues, no one but myself. So I found comfort in having agency over my own circumstances. And I slowly started to fix whatever made me unhappy.
The stuff you mentioned will bring you down for sure. Start attending to them and life will slowly get really awesome. No silver bullet of course, there are ups and downs but it feels so much better. And get help if you have to!
Maybe try sincere, old fashioned religion. It works for many. I believe there is something to it. (And done properly, it leads to helping others.)