The top on that Balance K looks like a basic walnut top, not superb in any way. Mike, just in case you don't remember the sound of your old S1 but, nothing sounds like a series instrument not even the signature instruments. They come close but no cigar.
You could get another series, use the batteries for power supply but they will fail after roughly 10 hours of use and your amp will sound like it's about to blow! Not fun.
If it was the only bass I was gigging with the power supply would not be an issue, especially to get that sound!