Insulating a drafty gas fireplace

I have a very drafty and underinsulated 1990s-era gas fireplace in Michigan. It is an 8″ metal chimney that goes up past the roofline inside of a framed siding chimney. The fire box is made by Majestic. Any thoughts on how I could reduce air inflow and increase insulation in an achievable manner, preferably without removing the siding?
I’m considering converting this to an electric fireplace, so I’m open to ideas that are not compatible with burning gas in it any longer.
Photos below.
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Replies
The Tag is pretty clear nothing combustible can be within 1.5 inches of the flue pipe. You could make steel baffles to bridge the gaps and caulk with fireproof material.
Note the listed clearances for the fire box.
Walta