It's not just a matter of how much sugar for what volume of beer, but also what the highest temp the fully fermented beer reached.
I would say 72* since it was hotter over the past few days (in NY). The average was 65-68*.
How much of a role does the temperature play?
I don't use beersmith but I imagine his carbonation calculator asks for beer temp. When you see that, it's asking for highest temp the beer got to AFTER fermentation was completed.
I use brewers friend.
5 gallons 2.5 volumes 60F needs 4.4 oz corn sugar
5 gallons 2.5 volumes 70F needs 4.9 oz corn sugar
If it got up to 80F it needs 5.2 oz
So it's not huge, but some difference. This is another benefit of temp control. When I bottle condition I know for sure what the temp was.
Something you can do is enter the least volumes you want at the low estimated temp and the most you want if it were hotter then prime with a number between those two. Like maybe min of 2.25 max of 2.7 and then maybe the average of those two sugar amounts is 4.5 oz for 5 gallons.
You are right though, earlier when you mentioned not doing your sugar calculation until you know how much is in the bottling bucket.
In the end I'll tell you the most common mistake. Not beings patient and ensuring that the beer is all done fermenting. Lots of people see the airlock quit, take a reading and it shows what the recipe suggests, so they bottle it up. But the beer still had some work to do and they end up with foam rockets.