Yes, turn your query into a user defined report.
You can right-click on your query result grid in the worksheet -
Then if you want a new one, i'd just keep the one and edit the report properties for your new query.
Doesn't have to be a grid either - you can have a report of type script. Or use charts. Or a lot more.
Works, but is there a way to run a report on a database while the connection is busy executing another query? (Unshared report?)
run your long running queries on unshared worksheets whenever possible, otherwise you'd have to create a new connection