I think the answer that works about the best is a combination of everyone's input.
1. Set the Line Width to a little smaller than your minimum trace/space (for me, 0.15mm) ... (The 0.149mm setting removes the interface where 2 planes connect and form small acid trap "dimples".)
2. Set the default flood hatch settings grid and smooth radius to 0
3. Apply the setting, pour the copper, then VERIFY the output!
4. While you're at it ... Set the copper plane properties too.
This fills in without creating slivers that violate my minimum 0.15mm trace/space requirement.