Actually, having your antenna 3/8 wave instead of 1/4 wave
will work better because it raises the feedpoint impedance
and makes it easier to match.
Either of the last two circuits (which are the same except
for component values) will work. Have you measured the
exact input impedance of your antenna? It is very difficult
to predict the exact value with a computer model because
it depends on the ground system, the effects of buildings
and the antenna support structures, etc.
Start by putting the capacitor in series with the antenna
and adjust it for minimum SWR. You may find that is all
the tuning you need. If the minimum SWR is still to high
because the input impedance is low (as it may be if you
have a good ground system) add the shunt coil and
readjust the capacitor for minimum SWR. If the capacitor
isn't big enough you can add some additional fixed
capacitors in parallel with it, or us a small bit of
the coil in series with the capacitor - but only as
much as you need to get a match.
So the final result might look like this: the feedline
is tapped to the coil at a point that depends on the
antenna impedance - perhaps 10 turns. Then, if your
capacitor is a bit small, there is another tap on the
coil - perhaps 13 turns from the grounded end - that
goes to the variable capacitor. The antenna wire
connects to the other side of the capacitor. Hopefully
you don't need the extra 3 turns on the coil.
If you have measured the actual input impedance you can
calculate the required values (as it appears you have
done.) If you have modeled the antenna you can still
do the calculations, but you will need to adjust the
values for best match.