Is there a way to get equipment to show up on the action list and mark off its uses?  Like if I have a magic item that I can use once per day, can I get that item's use to show up as a check box on my action list?

If you click on it on your character sheet - click customise on the popup window. If there isn't a checkbox that says "Display as attack" then no you can't. If there is then tick it.

Unfortunately no, doesn't seem like I can make a custom item that offers that...

You can from the Actions menu click "Manage Custom" and add a new action - but the problem with that is that it won't be linked to the item - so if you take off or unattune to the item - you would have to remember to modify the custom action or remove it to note that.

That would be the only way of accomplishing what you want afaik.