This! It should also improve efficiency.
Other things that have an influence:
- The exact value of the primary shunt capacitor.
- The toroid core geometry.
- The toroid material. There seems to be quite large tolerances, according to @HB9BCB, who published his results on this reflector with the same material (sorry, I can’t find it anymore).
- The environment and the height and configuration of the antenna.
- The length and layout of the “counterpoise”.
About your second question:
Good question and I don’t know the correct answer (the calculation for shortened dipoles or quarter waves doesn’t apply). But it doesn’t has to be exact. If the inductance is a bit higher, the remaining wire will be a bit shorter with a narrower bandwidth, and vice versa.
Some time ago I published a document describing a portable 7-band EFHW antenna, about 20m long, with a bypassable coil. How did I find the perfect coil inductance? First I estimated it, and then empirically removed some of the winding until it fit 
.
73 Stephan