Trays are a common "nestbox" in areas with overhangs for protection like this site. The sides just need to be deeper. I suspect that if they were going to do anything, they would have to build it, disturb the birds to install and fill with gravel and put the eggs in an artificially created (i.e., biologist digs small, shallow scrape with hand) and puts the eggs in. Best if done no later than mid-incubation as the birds are committed by that point and the eggs can tolerate being uncovered for periods of time (surprisingly long periods in the sun or if its warm). Depending on access to the site, difficulty to install, whole process could take between 10-20 minutes.
Question is, will/would they do it? I don't know the birds, don't know how tolerant they are of disturbance or how aggressive. But if I were comfortable that the birds wouldn't get driven off, I'd probably take the chance so long as I could remove the eggs and get them into an incubator if there was a problem. No later than mid-incubation might mean the birds would try again, so even if they abandonned the first clutch, they might try a second and the first ones could be hatched out and fostered in another wild nest somewhere. Its really a judgement call based on the adults. Our West Winnipeg birds in 2007 were in exactly the same boat as well as being totally rookies so I've run this scenario in my head already, but I knew those birds ...
I will see about contacting the Maine folks and see what might be happening ....