Can the divergence Mach be greater than 1?
The general perspective

I have so far seen multiple definitions for what "divergence Mach number" actually means (and worked with several of them), but it's usually tied to some empirical criterion with regards to drag increase with Mach number ($\frac{dc_D}{dM}$).

This means it's not telling you the Mach number at which shocks start to appear, but the Mach number at which somebody decided that the drag caused by those shocks is becoming "serious". It therefore stands to reason that this criterion will be different for different types of applications.

This means: For a given definition of divergence Mach number, and using suitably designed profiles, it may very well be possible to achieve divergence Mach numbers greater than 1 -- this means essentially that the shocks which form while accelerating towards and beyond the speed of sound are considered mild enough to not cause significantly more drag than would be expected if they did not occur -- again, for a given value of "significant".

The physics

The critical Mach number of a wing profile can, as you know, be increased by wing sweep. For an infinite, untapered wing at least, only the inflow component normal to the wing sweep line determines the profile pressure distribution. At 54° sweep, the effective Mach number is therefore just 58.8% (=cos(54°)) of the flight Mach number -- it'd be pretty easy to not even have shocks at M=1.0! However, real wings are never infinite (and rarely untapered), so there will be at least one shock at the tip/midsection/fuselage junction. That section at least will "see" the real Mach number, and "communicate" it at least some way to its neighbouring sections. That's one reason why Howe's equation has the exponent on the cosine. 

Prelim design

Reality is a bit more complicated than the Howe's preliminary design equation, of course, because using the c/4 line assumes that that's roughly where the shock ends up forming. If you have e.g. a delta wing with an unswept trailing edge, the further downstream the shock ends up, the less swept it will be, and the stronger. So it is based not just on flow physics but also on some assumptions about the ability and methods of the people designing the wing profile (in turn probably based on previously-built and tested wings)