Yeah almost all sets are either top or centre heavy by a large amount. It's still a mystery to me why this is

It's a decades-old tradition that perhaps compensated for the inferior technology of the past. For example, loosening the low strings makes them floppier and output more fundamental, to compensate for the low frequency response roll-off of vintage amplifiers.
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Originally Posted by Stilettoprefer It would be nice to get a set with a little higher tension also. |
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Originally Posted by Stilettoprefer I have to downtune from standard to BEAD occasionally because some jazz charts require a 5-string |
Do you want more tension because they feel floppy at BEAD? In fact detuning from EADG to BEAD halves the tension, it's a massive and extreme retune that I would advise against

No set of strings will feel good at both tunings. 50-105 is actually a heavy set, it irritates me how D'Addario and Ernie are calling it medium / regular

Medium should be 40-100. I wouldn't go much above 50 pounds on each string, that's very tight. I'm thinking 45 60 85 110/115 or similar? Roughly 45 pounds each string.