Maybe try a blue agate. That color will certainly pop. For me, carnelian has too much brown in it, and since I like bright red with a drop of yellow, carnelian is not a stone I would choose for a red.
I love colored gemstones (e.g. emeralds, rubies, sapphires....).
However, keep in mind, primary colors for stones do not exist in nature. You will never get a true red. For carnelian, it's either red with a drop of brown (e.g. blue) or red with a drop of orange (e.g. yellow). For emeralds, it's never a pure green. It's green with a drop of blue, or green with a drop of yellow. You just have to pick your poison on what secondary hue you want.
On ruby... I could go on for hours on the ruby. Ruby is my third favorite gemstone (after pearl and emerald). I have ruby pieces (all Burma ruby), and a perfect red is hard to find.
Without going off topic too much (I tend to do that, so I'm smacking myself now and limiting how many characters I have left to type about rubies before I put myself in time out

)...
If you are looking at rubies, I would suggest looking at Burma rubies and Mozambique rubies. You will clearly see a difference in the two. Burma rubies are the reference for rubies, and they are highly coveted. They tend to be darker and many are red with a drop of purple (e.g. blue). Mozambique rubies are a brighter red, and you will some that are red with a drop of orange (e.g. yellow). If you like the pure stoplight red color, I think you will like Mozambique. I'm not sure how picky you are with colored gemstones, but purist will only buy Burma rubies. If country of origin does not matter to you, I think Mozambique rubies can be very beautiful. Also, Burma rubies are currently banned in the US due to the political environment in Burma, so just FYI. It's not impossible to buy Burmese rubies, but they are rare.
Okay... back on topic about you...
Personally, if I were you and also seeing the bracelet in your photos, I would move on to another stone (e.g. blue agate).
You can't keep putting your wrist under a lamp to make that stone pop! And you can't keep using a cleaning cloth thinking it will brighten up! I've been there, and to put it bluntly, it just means you want the stone to be something it is not.
I personally feel you are forcing yourself to love this stone, and even with so many other ladies who love the dark brownish red (me excluded), you are still not loving it. It really needs to be love at first sight. I say give it up and move on.
If you do not like blue agate (I personally think it's the best colored stone VCA has out now)...
How about a VCA piece in another category? Do you really need another bracelet?
How about a necklace? Earrings? Ring? You have a beautiful MOP bracelet. You could get a necklace or earrings?
Or how about Frivole? I love love love Frivole! Talk about a collection that pops!
On blue agate... I'll do a little enabling here...
Blue agate will pop on your skin as it is a contrast color. The carnelian, with its tint of brown, blends better with human skin, hence it is more soothing and flowing to the eye if that makes sense. Colors like blue and green are a complete contrast to skin, hence they pop. Blue agate will do that... it will pop on you. You can't miss it on your wrist. Maybe ask your SA to bring in a blue agate piece and see if you like it.
Anyway, just some food for thought... Good luck to you. I am sure you will find something you love, and when you stare at it, it will be perfect!