I was the queen of mask issues when I first started diving, and maybe some of my fixes will work for you.
Is it the right mask for you? Have you done the sniff test with the mask on and the strap off outside of the water to see how well it seals? Does that mask leak without a hood?
You do have the hood OVER the mask right? You mentioned the hood moving under the mask, I wasn't sure if it started under the mask. Your mask should be under the hood. If you trim the hood to just above the mask, you will have less aggravation.
I was using an xs hood, but during my o/w, it was pushing my mask down from the top and breaking the seal. Once I trimmed the forehead of the hood, it was perfect. No more leaking or full floods. If it's your own hood, you can trim it.
Since I went scissor-happy with my first hood and people thought I would get icecream headaches, I bought a different xs hood which seemed fine above water with slight trimming, but was moving around on my head u/w and moving my mask with it, breaking the seal often. It was slightly big for me.
I then ordered another brand's xs which I couldn't get in Canada, and it was perfect, no trimming required. Since I knew no other hood fit me, I ordered 3 more for the future. I have to make sure my hood is pulled down very tightly or it will still lift off slightly underwater, taking my mask with it. So make sure the hood fits and is pulled down tightly.
I noticed a few times that my mask would suddenly leak when I had been wearing mascara the night before and had used eye makeup remover, which was a bit oily. My mask NEVER leaks except those times. Suddenly I was having full floods on those mornings. So I used a tissue to get any residue and made sure that my eye/cheekbone area was clean. No more leaks ever since.
Hope that helps you!