Ok, hate to answer my own question, but …
I gave the cutting plane some thickness (1/64"), created a solid. Now, I have two solids. Then use the “Trim” tool (Solid Tools). But, the order of selection is critical. Select the cutting plane as solid 1, then the vent as solid 2. Finally, move the cutting plane away, then window select the waste portion, delete, and you get this (no messy editing):
The only downside, is when using the native solid tools, the components get converted to groups. To avoid this, use Eneroth’s Solid Tools extension.
This really should not be so complicated, but it is. Or, maybe there is a simpler solution? For now, this works, using only SU native tools. 