No, Carryover Passive Losses do not affect the Basis of your house.
One option is to create a fictitious rental property (with $0 income and $0 expense), enter the carryover and say the rental was sold. That will 'release' the Passive Loss Carryover and it will show up on Schedule E.
Another option is to find the section to report "other income" and report it as a negative amount.
