Actually, I think the "Pixie" can claim a few fewer components
because it uses an IC audio stage, but either can make a simple
and compact rig. I've talked to at least one "Pixie" on the air over
a distance of 500km on 40m. (And one of the QRP clubs was
offering a surface mount version, the "smite", which was about the
size of a credit card and would fit in your wallet!)
I don't have my toroid info here, but your numbers look about
correct. For myself, I would take the pragmatic approach to finding
the right coil values. An extra 10cm of wire on each end of the
coil won't make much difference on 80m, so you can wind a few
extra turns and unwind the wire one turn at a time for testing. Just
resolder the end each time, without bothering to snip off the extra
length. This should get you close enough. (Actually, I'd probably
use 470pf fixed in parallel with a 365pf variable for the tuning
capacitor, since it is easier to trim the capacitance for resonance
than unwinding turns on the coil. At some point, anyway, you
should be able to make the circuit resonant at the output.)
To find the tap, you could tap the coil every 2 or 3 turns throughout
the middle third of the coil. Might be easier to arrange for the
circuit using two separate windings, instead of a single winding
with a tap - this allows you to adjust the turns ratio independently
of the tuning. If nothing else, put the tap in the middle of the coil
and allow extra wire on each end: you can then add a couple
turns at one end and unwind them from the other to move the
effective tap point.
But start with the tap in the middle of the coil and see how much
power output you get.