That antenna you mentioned isn't a bad model, but um... why do you want a full VHF-Hi/Lo section plus UHF? For TV, all you really need is a little 4bay UHF antenna like an Antennacraft U-4000 ($25 on Solid Signal), which you could combine with the existing antenna via a VUSJ (from Solid Signal).
Ok, so you have something 21st century for a receiver. While probably not as sensitive as 70s analog gear or a DSP-based tuner like the Sony XDRF1HD, they just work with no need for alignment.
For AM reception, you need an AM loop antenna for any kind of effective reception. I have a receiver with the "threadless" F-connector (looks like a BNC without the studs). Go to Radio Shack and get yourself a F-connector push on adapter. They work dandy.
I'd just plug your CM antenna into your receiver and see what happens. TC stations would probably require you to turn the antenna around. Given the FM Fool levels, I don't know that Stereo reception with full quieting or HD Radio (with the necessary receiver) is practical*, but it should be good enough to hear your favorite neo-conservative personality, especially since KTLK is so over-compressed. Maybe... just maybe you could get KTTC to lock while aimed at the TC.
If in the case that doesn't happen, installing a directional FM antenna (like an Antennacraft FM6) or getting a little 5 element VHF-Hi yagi could also work.
*On the impractical side, I'd try a tower and a Galaxie 32 http://ronsmithaerials.com/catalog/fm.html