Well it all basically works out, I guess -- I rounded lots of places, did
this in my head and came up with 240 ohms, somebody else said 280, another
one was 259.  I certainly agree that a 1-watt resistor is justified, this
guy will run warm!  I'll agree that it would be safer to use a 300 ohm
resistor, too.  It's just that these things aren't all that critical in
my experience.  The LED's that say they'll take 50ma typically have quite
a safety net built into them.  The resistors are typically 10%, so the 300
ohm guy really is "somewhere between 270 and 330".  One watt dudes are often
20% (which used to be the "standard grade", 10% was "silcer grade", 5% was
"gold" -- 1% ones were used in instruments).  A 20% one is 240 to 360 range.

As to running these in series, the current passing in LEDs is quite non-
linear.  I don't know if 7 will even light.  The caution about the glitch
in the regulator is a good one, though.  Why did you use the 2.5 in the
"5 x 2.5 = 12.5 < 14" bit?  later you use the 2.6 (which yields 13 and 
is closer!).  5 LEDs in series works for me -- I have yet to have one of
these arrays fried (I always expect it, though) and figure that this is
like a light bulb, allowing for it to burn out someday...  A single LED
in circuit with the resistor is pretty linear, since the resistor is
the major consumer, and as you start adding serial LEDs your risk goes
up, but so does your light, and the resistor can be made smaller (in 
power capability and size).  You might try six in series, see if they
light adequately (6 x 2.6 is 15.6 -- you'll fry more than LEDs with car
voltages like this).

Or just use a big 300 ohm resistor.  Or 280.  Or whatever -- it really
isn't all that critical.  It will get hot.

malcolm