2 weeks in the fermenter without racking after primary
No cold crash
The beer is generally cloudy when I bottle
Yes, room temp to carb up
2 weeks in fermenter should be enough to finish. It can condition in the bottles afterward.
US-05 is a powdery yeast, medium-low flocculator, it remains hazy for a long time.
The 2.5 week problems seem to be all carbonation related. The lack of it rather.
The yeasty taste you detect after 2.5 weeks means there's relatively a lot of yeast left in suspension, still busy carbonating. The yeast won't floc until the fermentables are used up. I'd raise the bottle conditioning temps 4-5°C and see if carbonation speeds up. Give it 3 weeks. That may cure all your issues, moving the time table from 6 weeks to 3 weeks after bottling.
The perception of being "watery" can be a lack of mouthfeel, due to lack of carbonation. Quicker carbonation would solve that too.
Cold crashing surely helps speeding up flocculation, with or without gelatin as a fining, but is not always necessary or even wanted.
It doesn't fix the slow carbonation, may well slow it down, it may be worth a try if haziness remains a problem.
After dry hopping I'd start with 3 days of cold crashing near 0°C and see if it the beer has cleared enough, up to 7 days if needed.
Try to avoid oxygen exposure/oxidation during the process. I sometimes cold crash in kegs, having CO2 in the headspace to protect against those.
Persistent cloudiness can also be related to a water chemistry issue, but it probably wouldn't clear after 6 weeks either.
The problem with 6 weeks conditioning Pales, and more so IPAs, is they are getting past their prime.