This isn't going to help the OP but for others experiencing the same in the future...
I had nearly the identical symptoms at first, went through all the same battery testing, charging, replacing nonsense. Coincidentally, I'm also in Northern Ohio.
For me the problem turned out to be the short cable running from the solenoid to the starter. It was corroded until only a few strands still made a connection, unable to handle the load, until the last strand went. Maybe I'm also having the problem mentioned in the Tech Service Bulletin and its merely a coincidence that I found this while exploring.
I haven't finished yet.
I did learn that these wires rotting out on Mazda 3s seems to be a common issue so something for you to keep in mind and look out for.
Did any of you that replaced the starter motor have difficulty removing it?
I'm trying to replace mine ( on a 2004 Mazda 3, 2.3 liter, automatic).
I do not have a (Mazda, Chiltons,etc) shop manual. I found at least one suggestion online to address it from above after removing the air box, etc.
but, so far I've been approaching it only from below.
The previous owner removed and did not replace the plastic splash guard/kick plate causing corrosion underneath. This should be a super simple job but so far I haven't been able to get past the first nut.
I've applied penetrating oil more than a dozen times, used sockets, wrenches til the points got too rounded, then tried extractor sockets (resisting as long as I could but, eventually,) even resorting to vice grips but all to no avail.
*top bolt wasn’t stripped, they were just dumb and couldn’t get it to screw in*
What did you mean? Wondering if I may be doing the same dumb thing?
Is there anything I could possibly be overlooking?
..or is this just a particularly stubborn nut?
The only other thing that I can think of left to try is putting a torch to it which I'm a little reluctant to do. Could it make things even worse possibly causing irreparable damage the stud?
Plus, considering how difficult this one is, I have no reason to believe the second nut --that I won't be able to see and barely be able to access -- won't be as bad.
I try to do things correctly, already have the new starter and got it at a good price but I'm growing tempted to just try replacing that wire with the starter still mounted ..even if to drive it to a garage but then, once there, what would/could they do that I'm not?
Has anyone here experienced anything similar with replacing their starter? Any helpful insight, suggestions, etc are appreciated.