Thanks for your thoughtful comments. I've read some discussions on the topic on science forums now, and though I still haven't made any calculations (and probably won't – I don't want to know exact values of things as they would likely limit more than help), I think it would roughly be like this:

1. Winds start moving as if the dayside is the equator and the nightside is a pole, i.e. cold surface winds towards the dayside, hot winds higher up towards the nightside. Nightside gets an ice cap, dayside gets hot rising oceans and a heavy cloud cover. The habitable zone is quite large, stretching both into day and night, but probably more into day. The poles still have their ice caps.

2. As the atmosphere condenses on the nightside, winds shift to moving only "nightwards". More and more water from the dayside gets frozen into the night cap, creating huge beaches of salt (should look cool on the map…!). Water beneath the night cap is pulled by the sun's gravity towards the dayside, creating some sort of interrupted cycle where all water slowly gets deposited on the ice. The habitable zone shrinks both ways, but because of the winds that carry lots of water, the land towards the dayside is kept from drying out, making the zone remain slightly more into the sun. The old polar caps probably melt towards the dayside, giving even more water flow into the habitable zone.

3. The magnetic field gradually weakens because of the slowed rotation and the solar wind blows even more of the atmosphere towards the nightside, where it either leaves the planet or gets trapped in the indent made by the weight of the night cap pushing the bedrock downwards. The seas are completely vaporized on the dayside, the rivers from the melting edges of the nightcap boil away in the desert. The habitable zone is very very thin and the air is hardly breathable.

Or something like that I have no idea how long each "step" would last, they would surely overlap a lot, and it's only based on forum discussions and Wikipedia articles compared with my intuition… But does it seem to make sense, sort of? And any idea how long it'd take to get to stage 2, where I think the map and eventually the story should be set?