I know what you're talking about, Zaid. With any deck finish, there will be certain angles at which the light will obscure the image on the card and show more of the card's finish surface because of how the light is being reflected. You should try using a deck of Bicycle Gargoyles under less-than-ideal lighting - all the faces were printed with silver metallic ink...
Most people "expect" an "air cushion" finish - in other words, embossed. Some will complain about decks that have smooth finishes, saying they look "plastic coated" and are cheaper and inferior in quality.
Nothing could be further from the truth. Regarding "plastic coated", ALL finishes are made of some type of plastic these days, except for the starch-based finish use in a small number of USPC decks. (Those decks are made with completely recycled paper using vegetable-based inks, meaning the deck is "green" and will decompose without leaving chemicals that don't break down easily.)
Pretty much every single CARC-designed deck made comes out in Cambric and Ivory Finish - embossed and smooth, in other words. The smooth paper makes for a stiffer stock and there's a bit less glide between cards, which some prefer for certain circumstances. D&D made their recent Steamboat reprints in only a smooth-surfaced version, no embossed.
The thing that will make the biggest difference for you is Magic Finish. USPC makes only two finishes which are sold under a variety of brand names: "standard" and Magic Finish. The "finish" in terms of texturing or smoothness USED to be applied via the finish using cotton or linen rollers to apply the coating, but these days the paper is embossed or smooth, so "air cushion finish" is actually a bit of a misnomer now. The cushioning is in the embossing, not the finish.
But back to my point - Magic Finish is the slickest stuff USPC makes. While most smooth-finish decks are terrible for fanning and have poor slip (major exception being the Aladdins), Magic Finish makes up for it. I have two decks that were made with Magic Finish on a smooth paper, and they perform excellently. Neither actually says Magic Finish on the box, but I know they were made with it and you can actually tell from the smell - Magic Finish has a distinctly different odor to it, a bit stronger than standard. It got its start on decks much like yours, black decks with a lot of ink in the paper, as well as decks with metallic inks (while some debate whether the quantity of ink affects performance, it's known that metallic inks do have a negative impact). The stuff is so popular, USPC made Magic Finish the default finish for ALL custom deck projects, free of charge - you actually have to ask for it if you want the standard finish.
You could easily get smooth-surfaced paper for this deck and apply Magic Finish to it without the performance suffering one bit for it. In fact, the smooth paper, due to having a surface that's not structurally-compromised by being embossed, is firmer and stiffer than decks made identically using an embossed surface. Dan and Dave's Steamboat reprints are amazingly light because of this - they were able to use a thin stock without compromising on flexibility and strength. And yes, that's one of the two smooth decks I was referring to that were made with Magic Finish. If you haven't already, pick up a pack of D&D Steamboats and you'll see what I'm talking about. I firmly believe that you can make your deck with pretty much the same stock/finish combination and the performance would be excellent.