@RunnyKine Thank you, yes, a minor change to the window function solved the issue perfectly. With the largest error now being on the order of 10^-15.

How perfect would you like it to be? As in what specific elements would you have liked it to have?

@YiWang Hold[A,B] Already has a working definition (it will hold the sequence of elements), so if you add some sort of tags functionality to Hold you need to either get really creative or break backwards compatibility. But really, I don't think that there is any reason why Inactivate couldn't just wrap holds around heads and activate remove these holds. But personally I prefer the distinction.

You're not answering the question which specifically asked for a solution without using conversion to floating point precision.