This is an epic post.
It is very relatable to every parent I think. Not parents, people, everyone. We all struggle with self concept and bounce these things off our parents in projections and mirroring or conscious decisions to be different or better than they were. I think we are fighting the part of ourselves that we don't like (the part we see so clearly in our parents). It is so much easier for me to judge and reject my mother than forgive her for the very same vulnerability / failing I see, no despised in myself. Hating her weakness and refusing to acknowledge I harbour the very same seemed a lot easier for a while, but eventually as the years turned I have started to learn. Yes only started. My oldest child is a teenager and I am still trying to figure out how to be a better role model. We never stop learning how to human. I haven't parented a teenager before, she is our first go at it. Her brother 10 years younger has already experienced a different toddlerhood, not due to preference but just life and circumstance and learning.
She is growing up before I have it all together, in fact it may seem it is all falling apart rather than coming together. But maybe that is life.
How do I make sure she knows she is of value? In the midst of all of lifes chaos, in spite of calamity. That she is always of value regardless of achievement or occupational engagement?
Maybe I can't. Maybe that lived experience is where resilience and life experience comes from.
I would like to wrap them up in the finest silk and put them on a comfy satin cushion to view the world but not be harmed by it. When they do go out into the world I'd place a force field around them that only emits positive thoughts and feelings that is transfused by osmosis to them in a steady unending supply...
Even if I could do that, of course it would result in being the very thing that they resent me for, regardless of my intention.

The every day grind makes ideals difficult to put into practice. We all need to pay the bills. I doubt that labouring brought your forefathers the sense of pride and awe you portray proudly. I wonder if they toiled with an internal dialogue of self deprecation for also not being a doctor or a lawyer. You portray their honest work as though they are marvel heroes, building this city's underground network with their bare hands.
Perhaps that is where the answer lies. Yes you also intellectualised their shortcomings, and that reflection is important, but how you felt about them, the emotion and pride came through in the description of the simple work they did. It spoke from the eyes and recollections of a child. A child will see you as a god regardless of your occupation. They don't care. They will even love you regardless of whether you are a great dad or not, they will. But how they will love themselves is determined very much by whether you believe you are great. Not what you believe they are, but how you see yourself. They model off our self concepts and how we value ourselves not by our occupational engagement.
Buying a home or passing on a pension, working a steady union job, these things are generational social change makes them unattainable, not you.

This rolls too easily from me in text, it is in fact just as much for my own benefit as it is for anyone who has endured me this far. This is my own challenge. I have had 2 years of sickness that removed me from being able to define myself by my career. I was a registered nurse, I was engaged in competitive sport and also for a short while some relatively high profiled charity work. Now I hear myself often say,
If we are a sum of the things we do then I am nothing. I am worse than nothing I am a burden you are better off without.
I have said this numerous times to my husband, and my children have no doubt on occasion heard me say it. I'm not proud of that, but for all our sake I refuse to be ashamed too, I think my children can benefit from not hiding flaws. To be honest my self worth was no better when I was winning at life. These things, job, social standing, beauty, they are decoration only. I think when I lost it all I saw my true self for the first time. I am still trying to figure out where to from here, but I have removed all the masks and pretence and the fair weathered friends don't call. There is still a lot that is up to me. A situation can be unavoidable but if I see it as failing or opportunity is really just about reframing. How I frame it and how we keep going regardless means changing how I talk about myself. That change will in turn impact my choices and behaviour and be of great impact to my family.
Our kids do see it all. Life is hard. They will be moulded by all the influences in their lives and they will closely identify with us in particular.

I hesitate to respond because I felt a post sized response coming on. I still have more to say, maybe I will post about it some time.
Thank you just like @bengy sparked your own thoughts, you gave me the same opportunity for reflection. I haven't been able to muster up much to post lately. You reminded me that I still have something to say. Thanks.

This is a photo of me a my son, taken a few months ago