I thought there was only flatwound strings in the 60's.
Rotosound Swingbass 66 strings were introduced, wait for it, in 1966.
Danelectro had rounds on their basses several years before that.
Wouldn't it have been easy enough to suggest some good flatwounds for the OP? He says he wants a 60's bass sound. I figure it would be easy for the experts on here to give a nice direction of guidance. There wasn't that many options for bass gear back then. lz4005, brother you need to work on your people skills. While I know you are extremely knowledgeable, people don't want the associated attitude that comes with your answers. Do you even hear how you sound? Stuff like: Um no, Lets try this one last time, or He apparently has no idea. You don't have to be Mr huggylove, but come on, this kid is looking to you for answers.
In a word, no.
50's was flats. 70's was rounds. 60's was the transition period between the two.
That's why in my first reply I asked OP to be more specific so he could get some relevant answers. Otherwise threads like this are always just people recommending their own favorite strings, not knowing if they're at all appropriate to the goals of the person who asked the question.
Instead of answering anything about what he was wanting to sound like, if he wanted flats or rounds, what kind of music he plays, or anything at all that might help us help him he replied with what amp and cab he has.
Giving irrelevant answers when you're asking for free advice is disrespectful.
Then he says he likes his sound now with factory (round wound by the way, so flats are bad advice) strings but also wants it to be better in some magical way.
OP doesn't know what he wants. He can't be helped until he can answer those questions. So he gets the answers he gets.
I know exactly how I sound. And I sound that way on purpose. Did you think my answers weren't intentional?