Is there a particular text that prescribes this line of thinking?
Well, brother,
I'm not sure which of the other options I suggested for interpreting Act.4:24ff your friend might go for, or if he'd just come up with something of his own. Where does Scripture give us an different kind of example or instance? Act.20:36 has Paul knelt down and prayed with them all. If he's of a mind to be resistant, because he's got a particular "kind" of argument or prooftext that he's waiting to hear, there's just no pleasing some people. I think this text, and the others I offered make a fairly good argument, provided one is inclined to receive it.
There are some folks who, when presented with the three or four options I offered (despite what seems "outlandish" vs. "sober," and despite an unwillingness themselves to propose some other explanation that makes better, or even just-as-reasonable sense) posture themselves as undecided, as if they're too spiritual to make a commitment to a reasonable sense, when there are ANY vying interpretations. Some people just want worship to be guided, not led; want lots of "leadership-participation" rather than followership-participation; and so they tend to read every place in the the parts-of-the-Bible-they-are-willing-to-receive-as-authoritative as confirmatory of their notions.
I fear such folks are coming from a "bad place," for whatever reason--from a bad church experience, or having had poor teachers who gave only partial explanations, or they've adopted an attitude that if God wants them to believe something he makes it infallibly clear to them by tailoring all explanations to their preset certainty meter. These come too close to Paul's description of a "divisive man," Tit.3:10. These are not especially teachable people. I do not assume that your Bible-study partner is like that, but presently I'm not seeing a bona fide deficiency in my presentation, and the potential objections you are raising seem empty of any real challenge, just maybe not "open-and-shut."
The individual and myself are in complete agreement here. The issue however is how this may apply the RPW as normative under the leadership of an elder in the Pastoral Prayer.
Again, this is an issue of "who should lead worship?"
I think this is more getting to the point. However I am concerned that he might retort that my presuppositions here are getting in the way of an exegetical treatment of these verses along with other assumption you previously mentioned, as noted above (see first block quote, "It's most reasonable...").
To which I reply, "OK, let's hear your exegetical rebuttal to my proposal. And we can go from there..."