Ozy: I assume your broadheads are on straight. Don't think I can be of much help on the spiraling issue. However, that won't stop me from taking a guess. I'm thinking your arrows might be marginally weak, which doesn't show up until you put the broadheads on. Going up in spine might help.
Re the small changes in one variable and not seeing any changes. Small changes can be overpowered by bad form, but just as likely is the fact that small changes usually aren't that noticeable. Big changes are or should be. Some folks say they can tell the difference in one twist of the string, 10 grains in arrow/point weight, a 64th inch change in nock height. Guess I shouldn't doubt them, but in 50 years of shooting with other folks, I've never met anyone who could.
Bigger changes, on the other hand, like a half dozen turns of the string, or an eighth-inch change in nock height or 50 grains in arrow/point weight should be noticeable, but they won't necessarily lead to better or worse arrow flight because most bow/arrow combinations are pretty tolerant of these changes.
If the arrow is tuned pretty well to the bow, raising or lowering the brace height a little isn't going to affect the quality of the arrow flight very much if at all. Likewise a little change in nock height won't either, nor will a little change in weight. Each may raise or lower the arrow's impact a little, and the operative words here are "a little" but the arrow will still fly true. And often, we're not accurate enough and/or our form isn't good enough to detect these changes, even with bare shafting.
I'm beginning to ramble. It's terribly difficult to diagnose a shooting problem without seeing the shooter shoot. All I can really suggest is take a deep breath, try to relax, and keep working at it. Keep experimenting, and don't be afraid to try some combinations that appear way outside the box. Good luck.