I can see why you'd be concerned about "aftertaste" carrying a bad connotation. I agree with @Barmar, however, in that adding "pleasant" or "pleasurable" to "aftertaste" should cancel any bad connotation.
As you're looking for a word that expands past the sense of taste, you might consider "mouthfeel," which is "the tactile sensation a food gives the mouth."
It isn't the most elegant word, but it does refer to what you're describing. It also doesn't carry any connotations, positive or negative, and it isn't limited to the "taste" sensation. You should be able to throw modifiers at it to make it suit your needs pretty easily.
On @lawrence's recommendation, I've added to my original answer.
I hope these two explanations will further clarify the term "mouthfeel" and how to use it. Both source articles have expanded information about the term and its various components. You can find a link to the source article at the end of each quote.
The term "mouthfeel" (or "mouth feel") may be used to describe the sensation produced when a food / drink is in the mouth or after it has been swallowed (as is the case with the drying sensation caused by astringent tastes).
Texture also plays a crucial role in how much we enjoy food. This has to do with how it feels to it — from first bite, to the swirl-around inside your mouth, to how it lingers after you swallow.