seems like an awful lot of unnecessary work.
My wife and I made a small garden a few years ago, we used unbroken ground covered in grass and weeds.
It was winter (in the south) so we scraped a bit of the dormant grass to begin with.
I rented a 5' tiller and tilled the area twice. My wife raked the few bits that were left.
I ran the tractor in the newly tilled fluffy dirt, and that's how I made the rows, the tires made the low flat areas, and the middle was the ridge to plant in.
When grass was cut on the weekends, my wife put fresh the clippings (grass, weeds, seeds and all) on the ridges and then eventually in the troughs for weed control. To my surprise that all worked well.
Pretty simple process really. No chemicals, etc. don't over think it.
Just till it this year and see if your family maintains care and interest, if they do and want to continue, address any issues next year.