routers have bits not blades. is that glued together? If it is a router won't do much. if you can lay that piece on the bench by itself then a 3/4 flat bottom bit set to the depth you want will route out that extra material. you'll have to put to eventually support the router with shims on each side.
If it is glued a chisel would be my first try. cut it into smaller pieces with a saw or utility knife so the chisel is not taking the whole thing at once.
This is what I did to cure a quad-divided Long Hive, the sides of which had bowed inwards a few millimetres after a couple of seasons stuck out in the weather - and which was just starting to jam the frame top-bars in place. Like yourself, I needed to take a few millimetres off the top inside edge of a box - in my case the inner edge of a rebate.
I used an L-shaped batten assembly which I'd been using as a table-router fence - but a flat plank would have done the job equally well, providing it had enough depth to be held firmly in place against the top of each side with sash-cramps.
It's obviously important that the plank is exactly level with the side's top surface, as the router will be running across them both, and so the combination of them needs to be dead flat.
A spacing batten (lighter coloured wood in the above photo) was chosen to space the router inwards, to create the amount of clearance required. If using a flat plank, then the spacing batten could simply be adjusted with G-clamps.
Perhaps this is clearer ? The plunge router depth was gradually increased after each 'run' along the rebate, until the desired depth was reached - in this shot there's still just a few millimetres to go.
By using a small diameter bit (around 6-8mm, if memory serves) there was precious little left at the ends needing the attention of a chisel.
During the cutting process, only one-half of the router base is on 'solid ground' as it were, so you need to be careful to keep the tool upright.
With your pitched roof, you'll obviously need to find some means of holding it very securely, no matter what method of cutting you choose.
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