Thanks for your great options and advice.
Do you think I should even Bother to add Flip up Iron sights?
How important is Co Witness?
Need 0 mag to co witness, right?
What about a magnifier I can flip out of the way like I have for my Tavor?
Yes, with any magnification you will not be able to co-witness back-up sights through the optic, as you would be able to through an un-magnified red dot sight or prism scope.
With some rifle scopes you will likely be able to have flip-up back-up sights mounted on the rifle, but because of the eye relief limitations of rifle scopes, the rear sight will wind up beneath the rear bell of the scope, so you won't be able to flip it up without removing the scope. This is also true of variable low power optics (LVPO) like the Vortex Strike Eagle mentioned. Even though it offers a pretty true 1X low power, you won't be able to use the flip-up rear sight mounted at the 12 o'clock position. The rear bell of the scope will be in the way.
If I read you correctly, you are really not all that interested in very rapid target acquisition for shooting at short ranges with both eyes open. Un-magnified reflex red dot sights and 1X prism scopes really excel for that application. A good LVPO with a true 1X low power will allow you to shoot with both eyes open for maximum situational awareness, but even good ones have eye box limitations that are much less tolerant of eye position than red dot sights, and in my hands at least, do not allow as rapid target acquisition as does a red dot sight. I do have the 1-6X24 Vortex Strike Eagle mounted on one AR. I have also found that relatively cheap LVPOs, within your stated price range, leave a lot to be desired. I tried one Bushnell optic in this price range which fish-eyed relatively badly at 1X, and the low power was more like a 1.4X which made shooting with both eyes open difficult. That got sent back.
A red dot sight in conjunction with a 3 or 4X magnifier on a flip-to-the-side mount is certainly an option, but I think you are going to have a hard time finding a decent RDS and a decent magnifier both for under $200. There are a number of good un-magnified red dot sights and 1X prism scopes within that price range, including the SIG Romeo 5, a number of Holosun units, and the Vortex Spitfire 1X prism scope. An option might be to start with one of these and add a magnifier later. With an un-magnified RDS and magnifier combo, you can swing the magnifier to the side, and flip-up and use your BUIS co-witnessed through the RDS alone.
The limitation with a RDS/magnifier combo is often the range at which you intend to shoot and the dot size becomes a limitation. The dot size on reflex type RDS is usually at least 2 MOA. With a true holographic sight you can get dot sizes down to 1 MOA or so, but those are well out of your price range. A 2 MOA dot will cover 2 inches of your target at 100 yards and 4 inches at 200 yards. This may or may not be a limitation depending on your target size. I personally find red dots of 2 MOA to become limiting when shooting beyond 100 yards, and I cannot shoot as accurately with them even at 100 yards as I could with even a low-powered rifle scope with a fine cross hair reticle. With a 3X magnifier that dot is going to look three times bigger. It will still be a 2 MOA dot, however, because the target will also be magnified proportionately, but any imperfections in the dot due to the quality of the reflective glass or due to shooter astigmatism will also be enhanced.
It also sounds to me that you are looking for an optic that is relatively compact and light weight. I think the most reasonable option would be a fixed power rifle scope of 3 or 4X magnification. A good one that I have used is the Nikon P-Tactical .223 3x32:
https://www.opticsplanet.com/nikon-p-tactical-riflescope-223-3x32.html
The nice thing about this scope apart from being light and compact and of very decent quality for its price range, is that it is short enough that it can usually be properly positioned of the Picatinny rail on the upper receiver top without the need of a one-piece cantilevered scope mount thus allowing the use of straight-up conventional scope rings which are considerably cheaper. You could buy this scope and a decent pair of rings and stay within your stated budget of $200.