> declaring on your own terms what you think the argument actually is isn't respectful

Which is usually a strawman tactic, and I agree both disrespectful and useless.

But... We will always respond to our own understanding of someone else's argument! That's inevitable, short of mind-reading. A habit of steel-manning the opposite case is a useful discipline for demonstrating respect - and, ideally, minimizing the necessity for clarification.

In practice, this means to make (to the best of your ability and understanding) an honest and accurate restatement of their case, and (if you see an opportunity - you won't always) a genuine suggestion that it would be stronger if it considered [x, y, z], before you attempt to refute it. You may not get it quite right, but you will have given your interlocuter a straightforward opportunity (as you say, conversationally) to clarify.

I think this is, given as I say that we're not able to inhabit anyone else's mind directly, the closest that we can rhetorically come to taking another's claim "at face value".