If you want something more "gym-like" than warehouse, construction or farmwork maybe kettlebells -- but there really is no substitute for dealing with large loads like ungainly bales or sacks of stuff or that have long wobbly awkward moment arms quite like moving lumber or sheets of plywood or drywall by yourself
If you tried, you could not be more perfectly...wrong.
Since I was brought up by a farm boy turned contractor, into a family of contractors, taught how to carry and manage loads like shoveling all day, carrying 100lb shingles up a ladder, or bags of mortar or brick, long before I got out, I learned to do everything you just mentioned. I learned a much more practical means of shoveling and carrying than most guys ever would and used more lower leg and back power. Add to that- that I lived in the Gym mostly power lifting and wrestling for fun.
None...of which prepared me for meeting a little man from Japan with a different idea. Which he kept saying to me was "Danny...different" while showing me things to do with my body. And none of that
I truly got till I STOPPED lifting and started training solo to change my body.
You are far, far from being the only one to have told me all this. I have yet to have a single guy walk through my door or train with me anywhere- who wasn't training internals- and could do anything we do. Most will tell you it feels unnatural and weird, and takes some getting used to. Just the way we train to carry our weight and walk or hit is counter intuitive. Even after being shown, they can't do it and default back to norms they and everyone else uses.
And *THAT* is the mistake in your idea of first training under heavy load. You default...every time.
Most experienced people already know that
This is why it so obvious to most that you..."don't get it."
But since you and your teacher know how I train and discussed my low understanding and where my deficiencies lay, why the questions? Let me come down so you can show me the way. Your post above clearly outlines a common laborers understanding of the martial body-one that you say you embrace. So I wonder in a show and tell, who will be showing the elementary school process and who will be pointing in the direction of the grad school process?
Have you talked to your teacher yet_______________________?