DigitalREV did this a while back. Pro Photogs with Cheap cameras. I think it's relevant to the topic matter.
Audio gear. A follow focus will only affect you where good audio affects your audience.
There would be a couple small differences. 60fps not slowed down will look like watching football on TV as they tend to shoot at frame rates for slow-mo. It may seem a bit jittery like Saving Private Ryan since the shutter speed is faster. Exposure will also be a factor when setting the shot but you won't notice this much in the finished product.
I would recommend a Canon C100 Mark I with AF. used on ebay is running around $1900, add a Ninja star Recorder and you have 4:2:2 8 bit recordings. You won't need external audio/adapters, ND filters, or any other "DSLR work arounds." Frame rates are the compromise here though as you won't have 1080 60fps, unless you want to employ a post production trick.
You could also look at the Sony FS100 used. The only reason I bring these up is they are actual video cameras, not a DSLR/Mirroless that can shoot video as well.
Functionality and ease of use can be a big part of a daily driver camera. I would say pick your top 3 and rent/borrow to get a feel for them. Just my two cents here.
My guess would be that you are having to stop your aperture all the way down outside? If that is the case I would start with a basic ND filter maybe 4 or 8 stops.
If it's not the case then I think Matthias and Elmoutasam have the right approach.
Just because I don't know your reasoning. Why are you buy a recorder that recorded 4k to pair with a 1080p camera?
Aside from that question here are my thoughts on both the Atomos and BDM 4k. If you went with the BMD you would only need to carry one time of media that is very compact and affordable. SSDs for the Atomos are fairly cheap now a days but they take up more space, you need a dock for them (more $$$), and the BMD seems slightly more compact than the Atomos Ninja Flame. (I assumed that Atomos because of the price point.) Those are just my initial thoughts. I would say rent them both once and use them, or find someone who has one and test it out. You won't really know which one you prefer till you get hands on with it.
Back to my question at the top. You could save yourself some serious coin if you got a 1080p recorder instead of a 4k one. I'm not sure if you are planning on upgrading cameras soon and that is the case, but that is my thought on that. Hope this helped in some way.