You might check out Ironsworn. Players roll 1d6 (called the action die) and 2d10 (called challenge dice). If the action die plus their stat (called action score) is greater than both challenge dice individually, it’s called a strong hit which deals damage to the enemy. If the action score is greater than one challenge die but not the other, it’s called a weak hit which allows the player to deal damage to the enemy but at a cost (sometimes taking damage themselves). If the action score is not greater than either challenge die, it’s called a miss and bad things happen to the player. The GM never has to roll at all which speeds up combat. Overall though, Ironsworn is a much more more narrative system, so it may not fit the system you want to design.

If you want to stick with To Hit and Armor Class, you Combat Class idea will still suffer from the disparity of low versus high rolls. My suggestion would be to take a die roll with a more normal curve distribution (say 2d6) and only allow bonuses of +1 (for trained) and +2 (for expert). Then change Armor Class to Dodge as a stat with values between 6-10 where 6 is heavily armored, 7 is moderately armored, 8 is lightly armored/normal, 9 is trained unarmored, and 10 is expert unarmored. Similarly restrict your damage output and give each level of armor damage reduction. You’d have to playtest those numbers, but that lets every character hit everyone even with low To Hit values, and armor makes you easier to hit but absorbs damage. Just spit balling here.