I got the weird taste since the beginning which I attributed to morning sickness. It got better when my morning sickness went away but still there and annoying sometimes. To manage it, I tend to drink cold water as I feel it takes the taste away. You can also eat sugar free mint sweets, helps too. I totally understand what you mean by eating to get rid of the taste. Sometimes when I am full, I will still snack on something just to replace that ‘taste’. Brushing your teeth also helps.
Not delivered yet but I suppose this will go away when giving birth. Am also in my third trimester. Almost there!!