If you used long scale strings on a short or medium scale bass, they will not be pulled to the proper tension, and they will sound flabby. It is critical to get the strings made for your scale.
I have several medium scale basses and buy my strings from
www.bassstringsonline.com - huge selection, great prices and service. No, I don't work there, just a happy customer. I understand you want tapewounds - if they exist, they will have them.