Rod,
I would advise that you do not to use a laptop screen as your light source, as I think this is where your problem lies. The eveness of a screen light is very suspect and will vary greatly from model to model, but in general there is a variation in brightness over the screen, mainly top to bottom. This is not very noticable, but when you stretch the image it becomes more obvious.
I use an EL panel, but at a pinch, shooting an iluminated white card as well as using a teeshirt type screen over the scope may work. Or I suppose putting enough diffuse material over the laptop screen may work, but the easy in which you can take flats with an EL panel makes an imaging session a lot easier and each exposure will be the same from session to session as you don't have to measure the distance from the laptop screen to the scope each time.
A very important point I want to make, if your not already aware of this, is that flats should be taken with the exact same optics, filter, focus, camera etc. as the main (light) images and they should not be moved between taking the lights and the flats. Any such movement can change the position of the dust, one of the very reasons you are taking the flats for to remove. In fact it will then add extra dust marks on your images.
Unless you have a cooled DSLR, there is no harm whatsoever taking darks on another day. This is because the sensor temperature will vary between exposures and thay can vary by about 10degC or more during one session anyway. So I have now stopped taking darks each session and just use one set to span a few weeks, after that the dark current may changed or more likely the ambient temp has changed by a marked amount, so just do another set.
What I do is record the ambient temperature and get a cool box with ice packs in till the air inside gets to the recorded temp and place the DSLR in there with an intervalometer set to replicate an imaging session, i.e. set the time to match the lights and the same interval between exposures and leave it taking photos in the dark cool box while I go to bed or if a long session go to work.
When you do take darks, or even the lights, ensure that the camera is in the dark or well covered as you may find that light gets in via gaps in the case or more likely via the connections. This can lead to patches on your images that may look like amp glow. To test this, with a body cap on the camera, take dark frames with a high ISO of the length you are likely to want to take. Take a few with a torch pointing at the camera from different angles. I was amazed at how much light was getting in via the connectors. You should also have the eyecup covered as well.
My DSLR (500D with full spectrum mod) has lots lost of bits of black gaffer tape all over it, but I no longer get light leaks!
Mike