Have you considered bone conducting headphones? Since they don't actually cover your ears you stay cool, and if you want to block out outside noise they come with ear plugs. I wear mine constantly.
Shokz OpenMove headphones are around $80 https://amzn.to/3LgYCq8
Have you looked at the Morserino-32? It does all of the things in your main list at least, as well as quite a bit more.
Another option would be the (tr)uSDX which is a 5 watt transceiver. Has all of the settings you are looking for, and can be set to practice mode without transmitting. Even has a CW decoder built in. This is what I personally am using to practice.
Hope this helps 73 de N5DEW