I posted this to the Tagboard a while ago, but I don't know if you saw it.
As story comics go, you can't get more story...-ee, er, -ish, than
9th Elsewhere. It's a truly well done manga style comic, that seems to be in every webcomic's link section. Please review it.
Another request is one of my more recent acquisitions,
Sokora Refugees. It's a story about a girl who gets pulled into a strange magical world under siege by demons, and ends up bringing back the intended saviour as a kind of magical stow-away. The book is already published in dead-tree format, and is now being re-released on-line one page at a time for free. Kinda like Girl Genius in that regard.
... Dude, you haven't tangented
A Miracle of Science? Dude

I don't know how that could have happened, 'cause to say MoS would be right up your alley would be like saying the president of USA lives somewhere around 1600 Pennsylvania Ave.
Speaking of Acid Reflux (you did. During the tangent of Kirabug's site in April.), have you seen
this and
this?
And I don't remember having seen
Antihero for Hire tangented...
...Or
Angel Moxie, though frankly I liked the early comics better.
Falcon Twin might be worth a look, along with
Farlight Saga and
Indavo. And don't forget
NSTA: Semper Vigilantis, and...
AAAAARRRRGH!!!! I read too many webcomics (my Comic Nation lineup consists of 135 comics, and rising, I've got the second largest list on their system).
OK, quickly, some of my favourites that I haven't seen here (all story comics, which doesn't cut down on my list much, as I share your preference on this point):
File 49 -- (Three kids with special powers find out they are the results of a genetic experiment that was abandoned 16 years ago. But now the government's special clean-up agency has reopened File 49)
Gunnerkrigg Court -- (Must see for yourself. Briefly, a little orphan girl is a student in a prestigous boarding school in a land full of shadows and magic)
Tales of the Questor -- (In a world shared with humans by humanoid raccoons, one raccoon-boy sets out to re-kindle the legends of yore by becoming The Questor)
High School Changed Me -- (Locke may be the 100 year old ghost of a 15 year old human boy, but that only serves to make him unremarkable when he is accidentally teleported to the strangest high school in the galaxy. A must for any fan of El Goonish Shive)
Kagerou: an Electric Manga -- (Whoa! One of the most well made stories on or off the web. Kano can't help but be very sarcastic when he is pulled into a magical world to be its champion. But all is not as it seems, and as we get glimpses of Kano's life on Earth, along with a disenchanted look at the public health system, we start to wonder if Grayworld is anything more than a complicated escape mechanism of Kanos.)
Wereworld -- (The alien warlords called Enigma kidnapped Steve, forced him to fight in their wars, took off his arm and eye to replace with cybernetic systems, and generally made his life a living hell. But Steve got the upper hand in the end, and with the help of MODOC, the artificial persona that used to run Enigma's strategies, killed their ruling council. Now Steve and MODOC hope to find a cure for Steve's terminal condition among the were-people of an obscure little planet, known to harbor a mysterious force called magic)