...I could not add more than four turns due to limited available space.
You need
fewer turns. Can you just pull the turns off one at a time and check
the resonant frequency? I've done this before with coated coils - pulling on
the wire as I unwind it allows me to break just the bit that is holding that turn
in place. Some acetone or fingernail polish remover might help to soften the
covering.
The charts for mobile antenna lengths and loading coils are in the ARRL Antenna
Book (and perhaps in some editions of the Handbook). There are also some
programs and calculators available online. You just need to know the length of
antenna below and above the resonator and the operating frequency. (The
element diameters make a difference, but probably not enough to worry about
since you'll be adjusting the stinger anyway.)
A quick model with EZNEC, assuming a 54" bottom section and 24" stinger,
suggests that 3uH would resonate pretty close to 28.5 MHz. As a comparison,
4uH puts me down about 26.5 MHz, so that might not quite match your
configuration, probably because there is a bit of space between the top of
the bottom section and the coil, which will increase the required inductance.