Yes, they work well together
This morning I received a comment on a YouTube video asking this question from Daryl Davis: "I've seen reports that the HB doesn't actually play well with umbrellas--no way to lockthe shaft, and the umbrella is cocked at an angle that takes it off-axis from the strobe. What's been your result with the Softlighter?"
At first, when I first worked with the Honey Badger back in August 2017 I did initially have a concern about the lack of a set screw to lock the umbrella shaft. In practice this has not been an issue at all. There is some sort of spring mechanism in the umbrella mount that holds the umbrella shaft securely. I also note that a number of other strobe heads rely on a similar mechanism with no set screw. Those include the Profoto B and D series and the Broncolor Siros L. As I said, in the 4 months I've had these heads this has not presented any problems.
As for the Photek Softlighter, I don't see any issue at all here. Yes, the umbrella shaft is not as close to the flash tube as on some other strobe heads. But in the Softlighter with its diffusion fabric (which some people double-up), I don't see that making a difference. The Honey Badger has a frosted dome over the flash tube and modeling lamp that helps spread the light 180-degrees within the umbrella. I could see this being more of an issue with lights like the Profoto B and D series that have a flat face on the strobe and limit the spread of the flash to around 75-degrees or so. The protruding dome on the Honey Badger (which is the same on the Interfit S1) is, to me, a very important feature. To add this to a Profoto B1 or D1 you need to purchase the Profoto Glass Dome for an additional $175 or so. And a new cover for the flash tube for $27. Total costs: Honey Badger (320ws) = $299, D1 (500ws) = $1416 Siros L (400ws) $2050 (battery operated).
Here are photos of the Honey Badger with the 46-inch Softlighter, both with and without the diffuser panel. I can see where the concern is coming from, but I have not had any problems with the setup with any of the Softlighters (36-inch, 46-inch o 60-inch). The umbrella fills nicely and the diffuser evens out the light across the fabric. The black ring around the flash tube that is used to connect the pop-up softbox that is is included with the purchase of the Honey Badger does make it a little tight to get the diffusion sock attached, but it also provides a way to keep the fabric from making contact with the flash tube (actually the frosted dome) without having to put a metal dish reflector on the head which would restrict the width of the light dispersion. It isn't an issue with the cool running LED modeling lamp in the Honey Badger, but I have melted the sock when using a Softlighter on an Einstein head with its extremely hot 250-watt Quartz-Halogen modeling lamp.
The bottom line for me is that I think the Honey Badger and the Softlighters play very well together.