I am not so sure about Adams as compared to Altherr. Adams has been pretty mediocre in AAA. Career 640 OPS, all of which took place at age 25 or higher. He had some decent years in his early 20s but never got out of AA until he was 25 and at that point I start discounting those age 24 and 25 stats.
He was decent in his 2017 cup of coffee in the majors but that was really the first time around the league and mostly against weakened late season rosters in meaningless games. I am decidedly NOT impressed by a 120 OPS+ as a 27-year-old outfielder in AAA in 2017. Then remember he was truly awful in 2018 in AAA (480 OPS).
This is kind of like the backup quarterback argument. Adams does a little bit of everything against mediocre competition and hangs around being average in the minors against younger kids. But there is nothing to suggest he would be a good major leaguer.
Altherr was bad last year, but even his bad is a 628 major league OPS. But he is one year away from an 856 OPS in 400+ plate appearances (so not merely late season). Lane Adams is nowhere near as good as Altherr.
"He has, twice, been a really good part-time MLB player." - That is just a huge overstatement. He has got 154 plate appearances total. So if you think 29 plate appearances is significant last year after he was awful in AAA, well I've got a bridge to sell you....
The issue with Altherr will be losing him if we don't trade Williams and Quinn is healthy. He is our 6th OF and without options will probably be lost if sent down. I doubt Adams would be lost, which tells you a bit about their relative value.