Thank you to everyone who offered their ideas. Toolman50: I'd like to offer you particular thanks for offering the simple but yet ingenious insight of simply drilling the affected holes straight through with a 3/4" bit, and then filling them once, with 3/4" glued in dowel material.
While I don't wish to bore people with the details, I will try to fill in the holes (at least with my explanations) below.
I saw this table on the internet, and without attempting to violate anyone's creative revenue, sought to recreate it. For me, much of the love of woodworking lies in mechanical projects that incorporate math. I don't sell my work (as if!!) and I am sure my product so deviates from this, which I attempted to recreate without blueprints, that no patents (if they even exist) were violated.
Okay, with that video seen by you, I concluded that the mechanics of my version--otherwise hidden from the table consumer's (i.e. my) view, would involve 8 lengths of (actual size) 3/4" thick, by 2.5" wide good quality wood, arranged in a star. Please see the picture. This would be time consuming to recreate--hence my desire to fix my mistakes, rather than rebuild from the ground up.
As is clear from my picture, many of the aforementioned holes, which lie at the end of each of the eight lengths, aren't centered as a result of "Stupid deliberance" on my part, to get them to line up with misaligned pegs that protrude from the Saturn like ring, (also shown) that rotates around the project's perimeter.
Should I have had the patience to do everything right the first time? Guilty!
For the terminally curious, at the end of the 8 lengths, the aforementioned holes connects with an arm (I've left only 1 arm still attached in the photo) with a length of 3/4" wide material removed from its center, that rides on these pegs, to allow the table's expanding leaves to emerge as the Saturn ring is rotated.
At the time I was inexperienced, lacking tools like a drill press where accurate hole placement and depth could be controlled and repeated, and most of all I was inpatient. I wanted to finish this project--which I will term a discovery build--and revisit it (what I am doing now) to fix my problems at some point in the future (i.e. now).
Of course the misplaced pegs and holes created unequally sized table leaves as the errors telescoped their way out from the center. Done correctly the leaves are 8 equally sized slices of a ring.
Today I own a large woodworking compass, and the knowledge from videos like this to find 8 equidistant places along a circle's perimeter.
..so, I will fill the holes in question, which are right now 3/4" wide in diameter for 1/4"depth, 3/8" wide for 1/4" depth, and 3/4" wide for 1/4"depth, redrill, reposition the pegs, recreate the arms and table leaves, and make this project right. This seemingly weird drilling pattern I just described was necessary so no nuts would protrude from the 3/4" thickness of each of the eight 3/4" X 2.5" points of the star.