Stitching multiple suns together

Question

I'm working on stitching together a midnight sun picture, where the sun is photographed every hour for 24 hours, so you get a 360 degree picture showing the sun's path through the sky. I'm using Photoshop CS6.

I've spent a lot of time positioning the images and removing lens flares and such from all of the pictures, and now I'm ready to stitch them together. However, I haven't been able to find a good blending technique. Right now, just to see how it will look, I've added a gradient to each picture to reveal the sun in the next picture:

The sky doesn't look very good using this technique. There are bands of darker sky between the suns, and the sun rays that stretch out sideways are clearly cut off before they reach the neighbouring suns. I've tried using Photoshop's Auto-Blend Layers with Seamless Tones and Colors to get a nicer sky:

This technique results in nicely blended sky and landscape, but the suns don't look so good. I would like the sun rays to extend further and overlap with the rays from the neighboring suns. When I look at only two pictures and set blend mode to Screen for the topmost layer, the sun rays stretch out and blend nicely together. This is kind of the effect I would like, except for the over exposure and landscape that does not blend well:

How can I blend the images together so that the sky is smooth, the landscape is clear, and the sun rays are allowed to extend into the neighboring suns?

Edit 2016-12-12

I've gotten some suggestions for using the Screen blending mode on all the suns, correct the over exposue with an adjustment layer, and combine that with one of the other methods for blending the landscape. This might actually be the best solution, but is really not straight-forward, as the exposure increses for each layer when using Screen blending mode (which is why I used only two pictures in my example). Here is what it will look like when showing 6 layers, all with the Screen blending mode:

Maybe a solution for this could be to "pair up" the pictures, so that I never have to correct the exposure of more than two layers (which in turn might consist of several already blended and exposure-corrected layers). What do you think?

Edit 2016-12-14

If someone would like to try it out for themselves, here are three images: 18:00 19:00 20:00

Answer 1

I suggest blending twice; the first 2 options where you didn't like the sun's treatment really produced a nice landscape (foreground). The screen blend you tried produces the suns overlap nicely; finish screen blending with all the images then use a gradient to place the previously blended landscape.

Answer 2

Once you have the images blended with a nice background (ignore the sun) put everything in a folder. then make a new collage where the sun looks good (ignore the rest) and put everything in a folder. Once done, use the blend if slider (if current layer is brighter than, position the dark slider so that everything but the sun is blended in, and then move the slider again with the ALT button pressed to soften the hard edge) to blend the suns with the background.

I just tried to do it with your posted files, but the image with the good sun's is too bright for it to work. i can post a sample if you post the image of the two suns separately.