Just something to think about, the length of the antenna has a direct correlation to its efficiency in terms of gain. I have thought of trying a multi-wire antenna off the same feed, so that way you would be close resonance on some of the bands.
tie point = O insulators for spacing so wires they don't touch each other from wind=8
Receiver____________O__________________________________________________________8
2nd Receiver wire____> \8____________8____________8_________________8
3rd Receiver wire_____> \8___________8______________8
the O being the tie point With insulators or spacers holding each separate but to the same connection wire.
As far as FM unless you are trying to get distant stations which are only line of sight anyway you are wasting effort other than a stronger local fed signal to your radio or TV, The problem with the new digital TV signals is that the old beam antennas had two different arrays, the longer for the now defunct analog signals (which have been moved to the higher frequencies) and the smaller array which all the signals of DTV are tuned to. So even though you have the older style, only half of elements are being used.
As far as using for short wave, you would be better off using the shielded coax as a vertical antenna going up the tower to the TV antenna. The shield would be connected to the antenna connection which should be ungrounded. Then use a separate wire to ground. The inner core wire is of no value because its shielded and useless this way.
If you are not using coax but twin-lead then it is acting as your antenna for short wave, because it is longer and picks up more signal than the TV antenna itself. However try the rotor and see if you have an improved signal strength as it to may be of help, but it wont be tuned to shortwave and you may notice no diffidence in directionality.
_________________
I'm a Science Thinker, Radio Tinkerer, and all around good guy. Just ask Me!