I'd like to know if my own version of a cell balancer will do the job
Your proposed balancer is similar to the one you posted in your own answer.
Your understanding of its function seems to be correct - the charge current is distributed to the cells depending on the discharge state of each cell.  A cell with lower voltage will get more current than a cell with higher voltage.
In that sense it will work.
The folks who wrote the article Overview of cell balancing methods for Li‐ion battery technology seem to think so as well.
This is figure 9 from that article:

It shows pretty much the same concept as what you have been discussing.
The problem is that it is a concept.  It is not a complete solution.
It is missing all the stuff it takes to safely charge a lithium ion battery.
In comparison, here's a full up system that will safely charge your cells and balance them:

It includes the needed protection for each cell:  charge control, discharge control, balancing, etc.
That diagram also leaves out a lot of details.  The details are in the datasheets of the named ICs.
What I'm trying to say is that a concept is a long way from a usable circuit and that lithium cells are not friendly subjects for learning through experiments.
By all means, continue with your concept.  You will learn a lot.
Keep the cells in a fireproof container, and be prepared to spend more in replacing damaged equipment than you save in building your own equipment.

Here's a paper in which a group at a university designed and built a balancer based on an IC from Texas Instruments.
Take note of the equipment they used in the development:

You are starting a difficult project.  It will teach you a lot.
I wish you luck.
Stay safe.