I've played a test-game until Literature (didn't pay attentioin to micro very much but didn't play too bad either) .
Results from that test game are:
- Capitalist can build the GL in 12 turns. It's the strongest choice if we want to get that Library as soon as possible and with as little effort as possible, because:
- Pigs-City has less Hammers than Capitalist (7
if assuming that we mine a Hill compared to 10
which Capitalist has) and therefor needs to either chop Forrests into the GL, and / or mine 2 Hills. I assume building it in this city would mean that we were making an effort while we could get it easily and without effort in Capitalist and
- Shark! It's astonishing, but that city needs "only" 17 turns to build the GL! I (we?) totally underestimated the Hammers of that city. It's on a Plains-Hill and it can work the Bronze, and thats 8
/ turn!
Test-game showed, that we can get a Library without problems in any of those cities, Pigs-city showed to be the most difficult city though, because we built a Settler in that city delaying the Granary in it resulting the city being small and unlocking the possibility of building a Library there later in comparison to Shark and Capitalist.
Interesting: Shark is so fast on the Library with having so much Food, that the city can even build a Lighthouse before the GL gets available.
Scary: Evil went WHEOOHRN very early in the test-game

.
Personal opinion:
Imo, we should build the GL in Capitalist and the Parthenon in Pigs city. My recent playing showed me, that Capitalist will be stronger in Commerce for a time that long, that I don't expect that moving the Palace to Pigs-city is worth it in this game. Pigs-city will only overtake Capitalist if we want it (so if we build Cottages on riverside Grassland Hills) , otherwise, the city will always be behind in Commerce. If you don't agree on the Parthenon at all, I'd still be fore building the GL in Capitalist, because stacking GPs makes sense to me. I also choose Capitalist for this build, because Capitalist is our Hammer-strongest city, and the city getting the GL should also be the city getting the NE, again, Capitalist will be faster there too.
Personally I also have no problems with a Capital that functions as a GP-Farm and as a Commercial city simultaniously, as I've played like that in various games already. Reason simply is, that the capital is the strongest city one has usually, so it can build the wonders with the highest speed, and capitals also tend to have a lot of food, which so they have the power to run 2 scientists even with working the cottages (also in this case, Capitalist has +6 Food with working all tiles except the Marble (and that plains-Hill on which I suspect a resource with a certainty of about 50%) , allowing for 2 Scientists, or even 2 Scientists and an Engineer.
Just to complete this and show the other options:
Building the GL and the NE in Shark will make us lose 5 turns on the GL and 2 turns on the NE. It'll result in 100% control to get GSs, but it's a definite loss of 68 (!)

and 4

/ turn! That's actually so much, that I think it can be safely assumed that with building the GL + NE in Shark, we'll miss on at least 1 GP in total over the cause of the game.
Building the GL + NE in Pigs-City comes with an effort, as to make the city competetive, we'd have to chop 2 Forrests before building the GL to build Mines on those Hills (WastinTime probably won't like this, because there's no garantuee that we'll get Math before aquiring Literature) , it again results in 100% control over the GP-Pool, it comes with a smaller loss in

if we enforce that build with chopping even more Forrests into it, but we'd still lose the

/ turn.
Seraiel