It’s a Quaker Moravian stove
You should post a picture of the stove so we know what model it is.
They made the arched top Moravian in an Insert, freestanding parlor and hybrid. (the hybrid has a round secondary intake at the top, front and center. Keep that closed for wood)
If it has grates (like flat plates on the bottom and a shaker handle on the right side) and a ash pan, it gets air through the ash pan door and is a hybrid wood/coal stove. They don't have the air wash the wood models have. Some models have a tag on the back with model number. They say wood, or wood/coal.
The wood stove models have slots through the doors under the glass windows. Is that the only air intake on your stove? Or are the air openings on the face plate below the doors?
Make sure there are no leaks into the stove. You want ALL incoming air to go through the air wash. Any leaks, like door gaskets or cracked cement in joints is air that balances the air pressure in the stove, taking away from what needs to rush into the intake at glass.
You don't have a fan blowing on the stove or across the front do you? Air movement over the glass can cool it causing problems.
Finally make sure the baffle is intact in the stove. Most had one in the top and directs heat forward.
The glass needs to stay hot. When starting it you may see condensation on the glass when first cleaned. If it fogs and takes a long time to dry off the smoke particles will stick. This is normal when cold. Water vapor is formed from burning the hydrogen in the fuel. Keep as much space as possible between logs to get air flow between them when starting it. Burn splits only, and keep the air wash intakes open until you need to adjust them closed more to slow it down for the needed output. If it gets dirty when first started many clean themselves by flaking off the glass after they get hot.
Are you using a stove pipe damper? You could be over using one. This will slow the air coming into the stove since it slows the velocity of rising gases up the stack. You want high velocity air coming into the air wash keeping smoke particles away from the glass. Make sure there are no deflectors or air guides missing or burned away. Some stoves have something to direct the air over the glass. If anything is missing the air goes straight toward the fire and up the stack instead of across glass where it needs to go. This is a part of good stove design, some are worse than others.
Does it get dirty near the top and stay cleaner at the bottom of glass? Or is the entire glass the same?
When they get bad I prefer the foaming oven cleaner. Let it soak until dry and recoat, scrape with razor blade.