So here's the division into wards. I did also try to trace the coastline off the 1970 ward map, and adjusted the Petri-Kirseberg parish boundary (which isn't actually defined all the way out on the maps) to go around the end of the oil pier.
We can quite clearly see which parts of the city were densely populated on this - there's a cluster in Slottsstaden west of the city centre (whose population was rapidly ageing at this point and would consist largely of pensioners in the 80s and 90s, leading to the nickname "Käppastan"), but other than that the big concentration is around Möllevången and Sofielund, which had been some of the densest areas in Sweden in the 50s and earlier, but would be relieved by huge amounts of social and co-op housing being built around the eastern and southern edges of the city, some of which we can see on this map (in Fosie and Västra Skrävlinge parishes, the latter being Rosengård).
In 1973, this shift has continued, with Lindängen appearing on the map (in the southwest corner of Fosie) for the first time and Rosengård continuing to be built up. There was also a decrease in the number of wards in central Malmö, mostly to get rid of the weird situation present in several parishes where two wards would be coterminous with one another while still existing separately - or at least that's the only way I can interpret the maps. Kirseberg also saw the elimination of a couple of wards, and the separate one for Kronprinsen (Petri 8) disappeared as well. Which is sad considering it went against the founding philosophy of the estate - the idea that residents should have all they needed to lead a full life without ever leaving the premises - but on balance I'm not sure having to leave once every three years would've done them much harm.
And here's that on an actual election map - the figures for 1970 aren't available online, so that one's going to have to come in later.
As you can tell, the constituencies don't come through very clearly, so I've added text clarifying which parishes were in which ones.
Not a ton has actually changed politically - the city remains split between east and west, with the exception of Husie which is more suburban and more middle-class than the rest of eastern Malmö, and as such is relatively marginal politically. One thing that is different from a modern map is that Limhamn still had its industries in the 70s, and still voted Social Democratic as a result of this. After the closure of the cement factory in 1978 and the limestone quarry in 1994, the area began to gentrify and reinvent itself as a seaside commuter suburb (only closer to the city than usual for those), and today it's both solidly blue and one of the most expensive parts of the city to buy a home in.
The other notable difference is the relatively strong position of the Centre, which almost outpolled the Moderates across the city. This was almost entirely due to a) the council elections having been synched to the parliamentary elections from 1970, which meant right-wing voters were less inclined to split their ballots, and b) the personal popularity of Thorbjörn Fälldin, who led the party to its all-time peak in 1973 even as the blue bloc as a whole narrowly missed a majority. Once Fälldin was gone, the Centre all but disappeared in Malmö - they left the council in 1988, and with the exception of one seat in the right-wing landslide of 1991, they didn't actually come back until 2018.
Since we don't have any real results yet, I thought I'd go back in time a bit and also try out the new municipal election format somewhere outside Sweden for a change.
In 1919, Berlin held its first-ever municipal elections under universal suffrage. For all its history up until that point, the City Council (known in German by the very handy term Stadtverordnetenversammlung) had been elected by the usual Prussian three-class electoral system, which gave a few hundred very rich voters equal weight to the poorest 80% or so of the city. Although turnout was always low, the SPD had a near-monopoly on the votes in the third class, so everyone assumed the city would go very deep red once the class distinction was abolished. But of course, by this point the SPD was splitting wide open, and both factions had some sway in different parts of Berlin - the majority SPD was strong in the city centre and the southern suburbs, while the USPD got the loyalty of the Wedding party organisation and quite a few of the north and east suburbs.
The election saw quite a low turnout once again, only 57,6%, likely because the National Assembly and Prussian Landtag elections had both been held quite recently and people were fed up with voting. The result saw the SPD and USPD on almost exactly equal voteshares, the latter edging out the former by a single seat. Put together, the two parties reached nearly two-thirds of the vote, with the remainder split between the four bourgeois parties now emerging - the DDP, the successor of the old left-liberals who had always dominated the higher classes in Berlin, only achieved a narrow third place ahead of the conservative DNVP, and over the next decade they'd only continue to shrink.
The council elected in 1919 was dissolved after just over a year. Some of my sources say this is because the new elections held were the inaugural elections for the new Greater Berlin council, but the problem with that is I can't find any data suggesting councillors were elected anywhere outside the old boundaries of the city. It's quite possible the outer districts did hold elections, but those don't seem to have been recorded anywhere, and this is arguably sort of good as it lets us gawk at the sheer insanity of some of the initial district boundaries. I'm not saying Hitler was good, per se, but finally straightening them out in 1938 is a definite point in his favour.
In any case, the 1920 election was itself thrown out and redone in October 1921. Unfortunately I don't have any local data for those (except for the district assemblies), so the next election I've mapped is 1925. This, then, is the first election for which I can find data covering all of Greater Berlin, and by sheer coincidence, also the SPD's best election result in the city under the Weimar Republic. With 32% of the vote, they won a clear plurality over the DNVP on 20%, and the KPD on 18% was prevented from winning any districts including their bastions in Wedding and Friedrichshain. In fact, the only districts not to vote SPD were the four southwestern ones, then as now home to some of the richest bastards in Berlin.
A new project. This one may take a while, and will probably never end up completely accurate - the only areas I'm fully willing to trust at this point are Greiz and Zeulenroda, because there happens to be a Wikipedian from there who's put together a very detailed set of maps of the area's territorial evolution. Beyond that, of course, urban areas are easier to find information on than rural ones, and I believe most of the "finished" parts of Sachsen-Anhalt have municipal borders as of circa 2005.
I found out that Sachsen-Anhalt has shapefiles of its administrative divisions at reunification available through their geographic survey office, so that state is now almost done (only the Harz remaining). I think the next step once that's done is going to have to be seeing if the other states have equivalent information available, because it's made things a lot easier for me.