Thanks, Christian.  I should have realized that cube handling must have somehow been responsible, especially with the big difference in equity despite similar raw numbers.  As is probably common in such cases, a rollout tells a very different story.

Curiously, if one knows (or deduces) the cause, the current output is probably more valuable.  It shows the relative rankings of the rolls without any cube "distortion" and lets you know that there's significant cube vig involved.  That tells you that a rollout is needed to confirm the hint and (perhaps more importantly) that a small change in the position will often result in very different equities.  It's important that players be on the alert for situations where evaluations are being greatly affected by the cube.

You knew I'd post again, right?  But naturally with only good news - an analysis of METs shows that doubles at this score can't be taken quite as deeply as for money.  This could easily explain why the aggressive play is wrong ATS (although the massive differences reported by 3-ply (and 4-ply) are still surprising).

So the only remaining question is whether I should expect the distribution of rolls to support the Hint's evaluation.  Simply put:  if the equity is a certain value (.978 here), why might none of the possible rolls be worse than that?

One last oddity and then I'll pipe down.  I figured hitting was not as attractive as at unlimited play since my opponent is at 3-away and thus we can never score 4 points.  So I changed it to 4-away and the bot said hitting was even worse!

This seems like a guarantee that something is wrong with its evaluations.

Another odd thing (feel free to ignore this) is that after playing the suggested move, I went into Evaluate and it showed virtually no difference between the three ply levels.

The key is probably something about match play.  If you look at the raw numbers in the original position, there's nothing to suggest much of a difference between the top two plays.  Yet the equity is much higher  for the safe play.  In money games, the evaluation is reversed.  Tim Chow suggested that this was due to badly missing the market in a match situation, but that seems odd to me.

I was skeptical of the 2-ply hint's evaluation so I played the suggested move and then looked at the distribution of rolls.  Sure enough, they didn't support what the hint showed.  I suppose I must be missing something but I'm clueless as to what it might be.

XGID=-B-DAaB-D---ba-bAbbe---A--:0:0:1:43:1:4:0:7:10

In the two screenprints, note the .979 evaluation for 23/16.