But you have no frame of reference at all about how long it took. It's not like they said, hey, I can see Arlong Park from here!
Episode one begins in the middle of the day. There's dinner and dancing going on. The Marines make impressive time on the attack so it makes sense that Morgan's base is close by. Coby and Luffy sail in late afternoon. Luffy frees Zoro and they sail off into the horizon at sunset.
After an indeterminate amount of time, the most conservative estimate being the next day, Luffy and Zoro are hanging out on their boat with no idea where they're going or when they'll get there. Luffy is starving, but that's not really a good indicator of how much time has passed. Luffy catches up with Nami by way of bird and sends Buggy flying. When they sail off, Zoro is so injured that he can't even walk. And once again, they sail into empty horizon.
The next episode opens up on a morning where Luffy is complaining about how all they ever eat is apples. This suggests at least a couple days of travel. You don't complain about "all we ever eat is..." unless it's something you've been eating for a considerable time. That afternoon they have lunch with Usopp and then learn of Kuro's plan. That night they plan against him.
(BTW, that was, at a minimum, Day 3. Looks like you're whole "3 Day" theory was even easier to disprove than I thought it would be)
The next morning Kuro attacks. The Straw Hats win. Kaya gives them Marry and they leave for the empty horizon.
Now the next episode is filler, but since this is an anime board, I guess it counts.
The next day starts with Usopp fooling around before painting the sail. Since we're talking hours of labor here, it's safe to say that this doesn't take place on the day they left the last island. Later that day they come across the 'treasure' island. Once again, they sail off into the sunset.
An unknown amount of time passes between then and the next episode. Luffy and Usopp accidently blow up Zoro's friends. It's nighttime when Johnny tells them about Baratie.
The next day (at minimum) they reach Baratie and Luffy accidently blows up Zeff. We meet Sanji, Gin gets fed and runs off, Luffy becomes a manslave.
Four days pass before Krieg shows up. There's much fighting. Nami runs off. Zoro gets slashed. Usopp chases Nami. Luffy gets thrashed and passes out.
Assuming he wakes up the next day (since a considerable amount of time must have passed without a visible change in daylight) Yosaku comes back and says he couldn't catch up with Nami, but knows where she was headed. Sanji packs up and once again they sail into the empty horizon.
At least a day passes because the next time we see them, Sanji declares it's lunch time. Since there's no way Nami arrives at Arlong Park shortly after with Usopp, Zoro, and Johnny close behind. Using Mohmoo to boost their speed, Luffy an Sanji catch up an arrive later. Nami's day goes from bad to worse until Luffy kicks Arlong's ass. Then they party all night. And then the next night. And then the night after that. (Zoro says "it's been three days now")
The next morning the Straw Hat Crew takes off an sails to the empty horizion.
That's a minimum of 18 days an they haven't even made it to Loguetown yet.
All of East Blue in three days? Yeah, only if you're like LPS and watching a different show.