I think you best bet would be to dry in oven, make a paste/purée, and incorporate that into your aioli.
I've also had luck using house preserved tomatoes (canned heirloom cherry toms) in oil, and using the oil to make aioli. I called it tomayonnaise because I am awesome. It was really good. I don't know how just simply poaching tomatoes in oil would work (the preserved ones I used were months old) but you might try that too.