One option would be to make the beam a flush condition. To get a 16' span with rafters you're going to be using at least 2x8s. That's 7.25" deep. If you were set the top of the beam at the top of the rafters and hang them from the beam (simpson or USP hangers) that buys you some space. Now an 11.88" LVL would only stick down 5-5/8" below the bottom of the rafters. (okay, 5-3/4"-6" with the additional slope over the 5.25" of beam) I'm not saying that a 3 ply 11x88 LVL with a 2.1E, bearing in a BC6 cap on 6x6s would work for your application, but the height tolerance would seem to add up in your favor.
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Fascinating interview around the technology. As someone who is generally skeptical of wild "zero carbon" claims, this was interesting enough that I would definitely go out of my way to see the process in person, just to learn more about it.