Congrats on the new pint size bass.
When you say the length sticking out of the body is 4.5 in, do you mean that is as far as the endpin will extend (pretty short...)? So you need about 6.5 in sticking out?
A few ideas:
-Trim a drumstick to desired length and stick it in there.
-Buy a metal dowel from the hardware store of desired length and diameter. File a notch in it for the stop screw and maybe put a rubber something on the end.
-Get one of
these from Gollihur. The stock Kay/Engelhardt is 1/2" diameter rod, though I think some are smaller. If yours is 10mm these ones won't work unless you replace the whole assembly. If you replace the assembly, you might need a luthier.
Hope one of these helps. Let me know if I misunderstood your measurements.