I also have Raynaud's Syndrome. It's gotten worse over the years. Here's what I do.
Before going out, I coat my hands, wrists, and forearms with Bag Balm. It's like Vaseline, but more waxy and less greasy. It's better than some gloves. Bag Balm is GREAT stuff for cold weather.
Next, I only wear mittens. Gloves constrict the fingers, preventing blood flow to capillaries that are already constricted due to the cold. Even the best tight fitting gloves make my hands cold. Mittens also let your fingers keep each other warm. Two pair of socks would do the same thing.
Anything that fits tight around the wrist also constricts blood flow, so you don't want gloves, mittens, jacket, or long sleeve top to fit too tightly at the wrist.
Finally, I'll use charcoal warmers in each mitten. They don't work great in gloves, but they're great in mittens because you can hold them in your fist while running. Here's a tip. Charcoal warmers last for 10 hours. If you put them into a ziplock bag and squeeze ALL the air out before you seal it, you can reuse them up to three times.
My go-to mitten is all fleece, but they are hard to find.
Before you buy a pair of mittens or gloves or run with two pair of socks, do this test.
Put one on.
Hold it up to your mouth.
Breathe out on it slowly. Can you feel the heat of your breath?
If so, the gloves/mittens are no good for running. Cold air is just going to blow through them.