Is bottle carbonation slow for these reasons?

[SMOKEU]

It normally takes only a few short days to ferment a low gravity wort in the primary fermenter. When we bottle condition we're only adding 2-4 gravity points, so fermentation shouldn't take long especially considering bottle carbonation is often performed at a higher temperature than primary fermentation.

Does it take so long because the yeast are already tired and stressed from the primary ferment, and there's a lower cell count due to cold crashing, and the yeast have a bad start due to starting off in an already alcoholic environment? Is that basically it? Can I speed it up by inverting the bottles every couple of days?

 

[IslandLizard]

Does it take so long because the yeast are already tired and stressed from the primary ferment, and there's a lower cell count due to cold crashing, and the yeast have a bad start due to starting off in an already alcoholic environment? Is that basically it?

You got it!

Can I speed it up by inverting the bottles every couple of days?

The yeast is still in suspension and priming sugar is dispersed throughout. I doubt inverting them makes a difference, but you will mix in the sediment again. It just takes 2-3 weeks, not much you can do speed that up.

You could add some fresh yeast when bottling, it may start off faster but that needs to settle out again when it's done, so there's goes another week, or two.

You can keg the beer or a part of it, so you can enjoy it, starting the next day until your (half) keg kicks or when your bottles are ready. Or bottle from keg.