If I was going to use polystyrene moulding, I would buy actual moulding probably from Omega, and not use cutting scraps. The reason I mentioned polystyrene is because you can must join it without an underpinner, because underpinning hugely subverts the strength of poly miters, which are basically chemical welds rather than glued joints. Properly made poly miters far outlive wood miters. But keep in mind that the price difference between poly and wood moulding for those sizes is negligible. The reason for poly in this discussion is because you don't need to buy an underpinner. With wood it's also a little tricky to drive either long or multiple nails up into tall moulding, some underpinners may not even be strong enough.
For poly I like the Freud LU92M012 12-Inch 72 Tooth Modified TCG Ultimate Laminate Cutting Saw Blade with 1-Inch Arbor. 90 bucks a pop. 10 inch models are cheaper. There are cheaper ones that I am sure will work OK. The Freuds can be re-sharpened around 15 to 20 times. No matter what anybody tells you, the normal ATB and similar blades that come with saws absolutely positively stink for cutting poly, no matter how slow or how fast you make the cut. TCG only, anything else is BS, and that includes some professional BS TCV blades said to be "for poly." Those "professional" blades are designed for continuously running saws, not for chop saws. Learn to make the required karate-chop cuts without fear, but as the blade ages you may need to slow down just a tad. It's all in the sensuous feel of blade-through-foam.
For such thin moulding in either poly or wood you would need to brace the back of the frame to something. Figure out a way to make your stiff backing board the real structural core of the frame. Otherwise I buy 1/2 inch by 72 inch aluminum strip from Lowes for a single cross brace on 6 foot frames, and two of those strips on 8 foot frames. I have a 1/8 inch hole punch designed for metal working, can't remember where I got it or what brand it is.
There is no technical reason to put paper on the back, the rear mounting board (or the gator on a normal treatment) is plenty to protect the artwork package. Backings are a pita because right away people punch there damned fingers through them, so why bother? The answer: because some people expect it. In my case, those people are SOL.
I would use two single hole d-rings on either side, and include a little note telling the buyer how to install the appropriate nails or screws in the wall, giving measurements and moral guidance. Any framed piece bigger than 6 foot wide should use that technique, whether poly or wood, but especially for poly which is more bend prone. The single hole d-rings allow the d-rings to swivel to compensate for less-than-optimal placement of the wall supports.