The seat post at 26.8 mm is not the most common of sizes, (we already know the approximate year) if it were 25.4 mm be a waste of time following this route up: but have your friend cross reference to Sheldon Brown’s excellent web site there is now a much expanded seat post diameter / manufacture’s cross reference, once he has a list of potential candidates then look each one up on Google check the hits & do cross checks on the photos, takes time, I’ve done it on a few occasions.

Assume the BB width is 68.mm, be another big pointer if its different.

As you say there must be a frame number somewhere