Bad Flats or Bad Field Flattener...or....

A few random points on this topic from this thread, both for you and for others with the same problem(s) later on.

~ Don't try to make assessments on individual sub frames (looking at individual calibrated frames after dividing the flat signal) unless you're looking for really huge problems; I've had countless instances where the ringing in my images (just like yours) is so faint that it's hardly visible in the individual calibrated frames, however in the final stack it's very disruptive and obvious. Stacking accentuates the features present in all subframes very heavily. Sometimes my 5-minute calibrated subs have looked perfect, even though the final stack of around 100-200 images looks terrible for this.

~ How did I fix it? Well for me the problem was a combination of multiple things.

1) Garbage focal reducers. I used a cheap $80 focal reducer on my SCT and got what I paid for. After countless hours of wrestling with different flat frames, processing tricks, etc., I found that my focal reducer was the primary cause of this kind of ringing. When I removed it (you should do the same and confirm the problem isn't present when it's gone), there was no such problem. I won't go into details of why these pieces of glass cause this, however they absolutely do in varying degrees. Sometimes it's still present, but just not enough to be noticeable. You can see my review of my offending FR here with almost identical ringing in the images. I ended up buying a $400 starizona reducer/corrector (for SCTs) and the problem is almost gone! Took a lot of dollars, but it's the only one that can stand up to this much integration time...

2) Varying flat frame integration times and techniques. I have settled on a weird, and against-popular advice, configuration for my flat frames that minimizes this problem further. Be flexible and this could help in the future. I now use (with an LED pad) flats with an exposure time to put the histogram peak about 95% of the way to the right, instead of at the middle. I know, that's not normal. But it's way, way better. For awhile I also used the highest ISO possible, although now I use 200 again just like my light frames. Take them immediately after your imaging session, not the next day!

3) Calibrate your flats! When I wasn't doing this, I had all kinds of over/undercorrection problems which makes the problem worse.  When I bias calibrated the flats (in accordance with the ISO of the flats, not the lights), I found substantial improvements. I don't use darks. YMMV.

~ Also worth mentioning to make sure your TOTAL flat integration time is, at the very least, 30 seconds, but preferably minutes. You'll add so much noise to your images without noticing it. Last night I used 50 flats at 3 seconds each. Don't do DSLR flats with exposures anywhere near a fraction of a second. It might calibrate fine, but you'll have tons of added noise to the result.
PS- your final result looks great!