With the super-chilled densified propellants, the Falcon 9 would be better off shorter and thicker to reduce surface area. However, the Falcon 9 must be ground-transported, which is why it has the same diameter restriction that the SST's SRBs had: 3.6 meter.
With no restriction on ground transport, the New Shepard can be as thick as engineering deems is necessary.
Lots of people have done the calculations. Poke around the Reddit Spacex forum and NSF forums, lots of discussions there.
> The first goal is to maximize aerodynamic efficiency, which means minimizing frontal surface area.
The fairing is already wider than the first or upper stages, so increasing those stages to the fairing's width would actually improve the aerodynamics.
With no restriction on ground transport, the New Shepard can be as thick as engineering deems is necessary.