There should be a way to promote militia to line infantry, because a single regiment holding three militia regiments off of the walls and surviving is massively impressive.
Capitol regions never Accept Surrender - but occasionally will accept an offer of Protectorate status while under siege, which amounts to roughly the same thing.
Not sure if it was an accident, but you moved militia off the cannon part of the wall on the siege defense. Don’t forget to take advantage of those cannons!
Thats the nice thing about Absolute Monarchies in Empire, you can replace your Ministers at ANY TIME, and just click and drag the guy from the list. You can even clear out the whole list if you don't like any of them just by replacing the same Office 4 times and ending with the guy you WANT in that office. So its pretty easy to deal with "government" Effects ,besides any from your King (less you SOMEHOW get the nobels to rebel).
Come check out Our Belgium Very Hard Grand Campaign set in Start Year 1830... The King has died ,a new King has been crowned ....King Walter I de l'Royaume del La Belgique