if a 4k HMI is the biggest light you have, your first challenge is creating a base exposure for the "cloudy"look that the 4k HMI can over power and look like sunlight. Even on an actually cloudy day it is unlikely a 4k will be enough light for that wide a shot. If it is just one shot you can grab quickly I would suggest shooting during magic hour after the sun has set and use the blue ambiance of the sky as your base cloudy look (you will have a very small 15-30min window or so to get the shot though)
If that doesn't work for you you are going to be very limited in options - if a 4k HMI is your biggest light I am guessing you won't be able to take on large scale rigging either and any other option would probably include a very large setup. For instance, you could shooting during daytime and rig large nets and flags over head of the set to cut down the light levels (with a shot that wide your in 20x territory though).
Your idea to put diffusion over the light to create the cloudy look might work in a close up, but honestly it is not a very good approach because the light on a cloudy day is very very soft. Think about what the source of light is on a cloudy day, Its the whole sky! so it is a very very big soft light - to mimic this generally people would bounce lights into a huge frame (like a 20x, or use balloon lights).
For the appearance of the sun all you need to do is mimic the look of the sun coming from behind a cloud. which when you break it down is really just a big light coming out from behind a flag. so all I would do is get a setup that works for your base exposure, position the 4k in a place the mimics the position of sunlight that you like and with a flag close to the lamp slowly raise it to reveal the light. the closer the flag is to the light the softer the gradation will be as you lift it, sunlight generally appears slowly and with a lot of gradation when it comes from behind a cloud so I would probably keep the flag pretty close and find a good trick for a soft smooth reveal.
the mirror idea is also nice and will help make a sharper source - depending on what HMI's you are using the beams can be kinda nasty looking so you might want to test some of the lenses if it is an HMI par or put it through a very light diffusion like OPAL to clean it up a little.
for the slit of light look I would place other flags around the light to control it and give it the shape you want.