This Brother 416 is killing me

I would put in a new bobbin and check the bobbin tension... you know the ancient hold in one hand and drop to another technique. not exactly scientific but it does work. and OF COURSE the machine messes up on the actual order! they often times do .. guess they don't like the pay or coffee or something but I have experienced it a LOT. seriously I think a simple fix... tensions. not yours, the bobbins/thread

Oh BTW I have had several of those machines and think they are really good! Kinda wish I did not sell them. But life happens.

I admire those that have some fancy numbers 70 g etc... same with cooking. I guess I have been around in this industry so long to just not be so scientific. lol pinch of this , dab of that, etc. I just hold the bobbin in its case and drop to another hand. same with top thread I just pull it through the needle, no guages just by feel. How come we do not teach that anymore? (maybe someone is making lots off these "gauges"?) cynical ha.
Bobbin winder. you wind your own? pretty awesome if you do cause most just use the boxed unless working on sewing with a regular sewing machine. OR if your embroidery is to be double sided so the bobbin thread needs to be the same as the top thread. Have done "stained glass windows" that way.

sounds like you got this! I use the aluminum sometimes but mostly just the paper ones

I spot a whole lot of issues. My major guess is its rotary hook timing and minor adjustments to take up spring. To eliminate variables change needles, check tensions and make sure you have your backlash spring installed in your bobbin case, polish your needle plate, and make sure there are no scratches on your rotary hook... But most likely its hook timing.

Starting with the test run materials...
You ran it on a woven material when the customers product was a knit. This can contribute to resistance differences when doing test runs as well as changes in edge quality and some fabrics highlight problems with machine setup better than others... Just a note.

Second On the test run on the upper right hand corner of the outline of the circle there are missing stitches,
And on the back side On the pigs chin and the lower "left" hand of the inner circle outline, and the upper outer outline you have uneven bobbin show.

On the sewout both the black the red and the orange that I see have way too much top stitch showing.

The most likely problem is that Your machine is probablly not tuned right... or more accurately isn't perfectly tuned to itself well.
More often than not its a problem with the rotary hook timing whether its too close to far or timed a degree or two off from what your machine wants the timing to be at (doing it by book specifications is nice but more often than not a machine runs better if its tuned to where it wants to be, 202, 200, 201.5 some heads just run slightly different). Not only that but needle to needle it can have minor variances and directional variance in the stitches...

Wovens and knits have different friction resistances... In an ideally tuned machine it wouldn't matter cause the tension forces are timed and in balance to overcome either or and the material doesn't effect the thread much...

If your hook timing is off or early by a degree or less or the distance between hook and needle is off, you can get missing stitches and in this cases you can get an instantanious pull prior to wrapping arround the hook. the hook is pulling the thread THROUGH the take up lever and spring instead of the take up lever feeding the thread into the fabric.

I need to do some tests to confirm this statement so take it with a grain o salt On the woven, extra thread tension and pull gets transfered to the fabric while the needle is in the fabric causing little thread to get pulled through the take up lever, but when being pulled back out twill tends to maintain the hole created causing lesser friction as the thread gets pulled back through to finish the stitch, thats why you get offset bobbin show. Less thread gets pulled through during the initial pull and you often get a managable stitch on thin wovens.

On Knits you have less initial friction causing more thread to get pulled through due to instantanious velocity transfer of the rotary hook into the thread... But because knits tend to rebound the hole created by the needle is smaller causing higher friction and inconsistant friction depending if the needle hit a cross over point of that knit pattern, notice on the back of the sewout there are black loops and orange loops in the fills... Thats where the hook pulled additional through and the take up lever couldn't pull it back out...

Finally the slack thread problem, if there is slack thread, more often than not you get 2 problems the first problem being that the backside starts to birds nest and if birds nest gets overcome then you have additional friction due to thread build up compounding the issue, the second problem is the twist in the thread that happens when coming off the cone will cause the slack thread will cause the thread to wrap around the needle but this usually only happens after a trim, or if there was a thread break.

oh my gawd... lol that is a lot to digest! but hey, you know what you are talking about so cudos!! just dummy it down for the rest of us sometimes please??