I wouldn’t permanently install anything outdoors that isn’t designed for it, but I live in a climate that gets both >100 F and subzero temps. If your local climate is mild enough and they stay 100% dry, you might have better luck, but it seems like a big risk of turning nice speakers into trash. I definitely wouldn’t install anything ported or those speakers will end up as a home for something.
I’d suggest getting an amp you feel confident about and then trialing speakers bought from somewhere with a good return policy (the already installed AW6500s with the new amp first, of course). Dynaudio makes outdoor speakers, as do Kef, Focal, B&W and several other reputable companies. Can’t say I’ve heard many, but they’ll at least probably sound different than the AW6500s that aren’t quite making the magic you want. Also agree that an outdoor sub might free up the compromised outdoor speakers to sound better in the non-bass frequencies, especially if the amp has a high-pass filter to not run them full range.