Original User: dananrg
To solve problems 1 and 2 above, we utilized "problem #3" behavior. As well, the mismatch between layers in the MXD and layers present in the 'select sub-layer to query' dialog was our goof (we'd forgotten to turn on the Shape field for one layer).
Here's how we got our desired user experience:
We turned the Shape field off for all but one layer ("State Maintained Routes"). This way, the 'select sub-layer to query' dialog gets bypassed, leading immediately to the Query Builder--with only one layer enabled for querying, there's no longer anything to choose from. And since there is no Definition Query defined on this particular layer, when a user clicks on a field and gets a list of domain values to choose from, this now makes sense contextually; e.g. they are no longer limited by a Definition Query and can search for whatever they like.
My apologies--our mistake. However, it would be nice to see more detailed documentation about the new Query feature. Better documentation, or a cross-reference to relevant ArcGIS Server documentation, would have saved us some time. Our request for Legend-like enable/disable functionality was there all long--it just took a bit of trial and error to discover it.