Shalom!

I have tried to find mention of your Safek in the Mefarshim. The closest that I can get is that the Minchas Chinuch has a Safek if the Psukim are a Mitzva (that is to say that even without the Psukim it works) or l'Ikuva (that is to say that without the Psukim it doesn't work). So, on the side that the Pesukim are not l'Ikuva, it would seem that they could still bring the Egla. On the other hand, even if the Psukim are l'Ikuva, other Dayanim could say the Psukim` of course, this may not be true as those speaking are speaking for the Beis Din as a whole.

I think that the proper perspective on the question is that each Beis Din put a framework in place in their town that travelers and sojourners should be adequately cared for and if this was not in place it was gross negligence, so the probability of this scenario was extremely small. But this is only my conjecture, and you have every right to adopt the saying of the Yeshivos, "a strong unresolved Tzorech Iyun is better than a weak answer."

Shimon Brodie