I think
Second thoughts, you would want to set the iso range low, 80 say, so that as light increases it drops the iso instead of stopping down aperture. That would tend to set the lens wide open if, for example, you are shooting a bird in flight against the sky. If your lens can handle wide open, this would work.
I may be reading your mind, but I suspect you are trying to keep shutter speed high enough but have the rest of the settings follow without having your iso go too high. I found with TAV mode that I ended up in practice with too many high iso shots with the attendant loss of quality because I wasn't quick enough to twiddle the two dials to find the sweet spot. If you are following a bird in flight against trees or mountain backgrounds, it is impossible to twiddle. Auto iso in tv mode might work ok, and you can bias towards stopped down aperture by raising the bottom limit of the auto iso range.
Having lenses that need stopping down to give any quality at all, I've tended towards AV mode and got reasonably quick at adjusting iso to get a shutter speed that I want. In practice I end up with lots of movement blur but no CA. I remind myself that shooting birds is one of the most challenging subjects to not become disheartened.