I don't recall them ever getting "shut out" on offensive tackles. I remember it as all the talk there was that they specifically wanted to address the LG spot and that's what they got shut out of. That was the year where they traded Shaq Mason and penciled in Onwenu at RG. They had Trent Brown and Isaiah Wynn penciled in at the OT spots and then Andrews at C. On paper, they had NFL caliber players at ever position except for LG - it was their clear and obvious weakest position.
From what I recall, HOU taking Kenyon Green at #15 and LAC taking Zion Johnson at #17 were higher than expected and there was a huge drop off in OG prospects after that. But they had pigeon holed themselves into picking that spot specifically so even though he was a reach, Strange was the next guy on their board at a spot they felt they needed to come away with a starter at. Hence the trade back and overdraft. I might be wrong, but that's how I remember it.
Textbook example of why drafting for need is silly and why you should use free agency to give yourself passable options across the roster so you aren't ever that desperate. Which BB traditionally did really well over the years until the end, but so be it.