It may be that the frame was originally designed to have slats span the rails, and not have the mattress (box spring) sit directly on the rails. This would have lifted the mattress up a bit, and possibly allowed it to ride over the bits that are giving you trouble.
This was one persons solution:
![enter image description here](https://i.stack.imgur.com/hXtNC.jpg)
First I would go with warm white lights not the cool white, I think it makes a softer look to the bedroom.
In terms of the switching, yes a push button switch would work fine, you just have to make sure that the switch is within spec for the lights used. I have rather opted for a dimmable solution with my childrens beds. since they like to have some light at night. a good option here is this:
![enter image description here](https://i.stack.imgur.com/iWza1.jpg)
Its rated up to 8 amps, so if you look at the strip in your post, it consumes 2.5amps per 5m section used. (provided that you buy a transformer that can supply up to the required amps (ie 2.5amps per meter) -- you can buy a smaller amp transformer, but the lights will not be optimally bright at the highest level.
Your switches are only rated 3 amps, which means you can run about 5 meters of your spec LED Strip. -- Also to note, I would go with a stronger LED strip, generally 1 amp per meter is a nice powerful light (then you would only need a meter per child)
Another thing to consider, is the use of the 3color led's whereby you can have a color chooser.. but that may be getting too complicated.
Your series vs parallel question: You must definitely hook up the two lights in parallel, but just accomodate for the increased amps which will be required. The lights will draw the amps needed so you cannot really blow anything (its the volts which will blow the lights)
Finally: I find that the higher power led strips get a little warm, (meaning that the sticky tape sides start to get less effective over time). would be best to stick the strip to a metal surface if you could choose (it would act as a heat sync)
I actually ended up using a Chinese paper lantern to put the led strip in, it looked quite nice.
![enter image description here](https://i.stack.imgur.com/bizTi.jpg)
Best Answer
Since you are cantilevering off the wall, the verticals must be exemplary. This is a very significant structural side load. I would consider Unistrut, and it must be tied to studs proper, never to drywall itself.
If the stays (diagonal cables) came the whole width of the bed, they would carry up to 100% of the occupancy load if the person is rolled out against the edge / sitting on the edge at the top of the ladder.
If they are less than the full width, then divide by the fraction of the width. For instance if they come out 30% of the ways, then 185 lb / 0.30 = 616 lbs. That's static load; dynamic forces could be much more.
As a practice you should engineer for many times the weight.
Keep in mind this same force will also bear on the wood, so you're talking about a tremendous force at the attach point. One way to handle this is a steel plate along the outside, screwed into the wood at close intervals. Steel is very strong but is a wiggly worm. The wood keeps the steel straight, greatly increasing its strength.
Also, you may want to provide a means of adjustment to the cables.
All in all, you may be better simply installing high beds that do not move, and creating desk, storage or living space below the bed.