The position below could quite plausibly arise from a position that was recently posted here. GNU tells me that there are 637 legal moves, none of which is a whopper by the usual definition of a whopper as a 0.1+ error. I've displayed the start of XG's list just to illustrate that some odd-looking plays like 5/3 2/1(2) are near the top. So 416 letters aren't going to be enough. I'm not sure which 221 plays aren't covered by nactation but maybe you can identify one.
This was just off the top of my head. If we allow contrived positions then my first attempt yielded a position with over 1600 legal plays (not displayed here). With some effort I would guess one could construct a "reasonable" position with over 1000 plausible plays.
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| XGID=--B--BBB-B-----AA-AAA--ee-:1:1:1:11:0:0:0:7:10 | ||||
 to play 11 | ||||
is Player 2| 1. | 4 ply | 20/18 7/6(2) | eq: -2.072 | |||
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| 2. | 4 ply | 19/18 15/14 7/6(2) | eq: -2.072 | |||
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| 3. | 4 ply | 20/19 15/14 7/6(2) | eq: -2.072 | |||
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| 4. | 4 ply | 5/3 2/1(2) | eq: -2.073 (-0.001) | |||
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| 5. | 3 ply | 19/17 7/6(2) | eq: -2.073 (-0.001) | |||
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| 6. | 3 ply | 19/18 7/6(2) 2/1 | eq: -2.073 (-0.001) | |||
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eXtreme Gammon Version: 1.21, MET: Rockwell-Kazaross