The working answer to your question is yes, and drop the hyphen, and while you're at it, drop the quotation marks. Like new is perfectly familiar diction, which means that it doesn't require typographical emphasis. Quotation marks are used to dr aw attention to a new coinage or an old word used in a new way. In this case, the quotation marks are likely to make your readers think that you are lying about the condition of the floors, and that they are not like new at all, but rather that the owner simply wishes them to be perceived as like new. The rules generate a mess even worse than the one you supply.
All quotation marks fall outside terminal punctuation.
It has the character of a grammarian's party joke. After all, the punctuation is the least of its problems. Even orally, you can barely follow the words. I have a general question about the use of quotation marks. But since I don't know if the prosecutors actually said those words, I'm not sure what to do.