Well, considering that these "cheap USB TV tuners" were never really designed for this kind of actual use - but they do amazingly well even so - you can't actually expect the same level of performance for many reasons but I won't go into every single one of them. The basic gist of things is to use something like a traditional NOAA weather signal in the 162 MHz range to get yourself up and running. Since you live so close to an airport you may be able to pull one from there since that's where most of the transmitters are located in the US (major international airports but also regional ones too with pretty good coverage of the entire US but you probably already know this).
Anyway, I personally either use that (when mucking around in the CivAir or VHF-Hi range (118 to 174 MHz combined) for setting a calibration - I have the older RTL sticks from NooElec with no TXCO so I have to deal with the thermal issues, if you have the $25 sticks that more than likely means yours are using a TXCO and will do much better but still can require calibration out of the box of maybe 1, 2 ppm at most to get as close to being "on frequency" as possible.
For UHF I tend to use the ATSC signal here in the US at 470.310 MHz (Channel 14 as it's labeled) for such calibration purposes and that one works well for me even through 940 MHz most of the time. I have my two RTL sticks plainly labeled (one has a 49 ppm offset and the other is 56 ppm) and I've never really had issues with either of them in the ~2.5 years I've owned 'em now.
If you've gone through all the setup and testing which apparently you have, the only thing I can suggest at this point would be try attaching the external antenna directly to the RTL stick (if you have the proper adapters) - don't use the switchbox at all for this test and see if there's any potential increase in signal levels. If there is, and it's noticeable, you could have a faulty switchbox - could be as simple as disassembly and cleaning the internal contacts (if it's a really old one), blowing it all out with some compressed air maybe, or simply redoing all the antenna connections after cleaning off the actual connectors with a wire brush or something. Anything is possible at this point I would say so it's just some actions you can take to confirm where there might - I say
might be a potential signal drop to the RTL stick itself.
For myself personally all my hardware is inside, would love to get an antenna on the roof of my apartment building (I'm on the 3rd/top floor so it's like 6 feet above me literally but they won't allow me to do anything on the building structure itself) which would make a big difference for me I'm sure. My central location in downtown Las Vegas does get me most anything valleywide for ~20 miles in any direction to the sides of the mountains that enclose us here, with major tower sites to the southeast and on some of the taller casino-hotel structures as well. I don't miss much but even so, more is always better.
As for airport/aircraft listening I'm also almost in the middle of two airports: McCarran International about 6 miles due south of me and Nellis AFB to the northeast by about 6 miles as well. McCarran's ground traffic is basically blocked by a very large concrete/steel/metal/glass structure directly behind my apartment building sadly but Nellis I can pull in to some degrees without issues. Whenever the Thunderbirds are out for practice I typically fire up the RTL stick and SDR-Console aka SDR-Radio and listen in to the lead pilot as he calls out the maneuvers. I've taken my laptop and the RTL stick along with my OCFD out on the balcony before and had a tremendous increase in signal reception but that's obvious because I live in the rear portion of my building and their signals have to pass through an entire half-block of physical structure (even though this place is made primarily of wood and sheet-rock more than steel) before it gets to my apartment.
But test the direct antenna connection to the RTL stick and see what happens, might notice something, might not. For most people the preferred method of adjusting the gain is to use leave the RTL AGC and the Tuner AGC
off and only using the slider to adjust the gain as necessary to keep the noise levels as low as possible, but there could be times when you'll kick one or even both of them into action for temporary periods.
You may end up coming to a point where using a dedicated antenna designed for CivAir/MilAir might work best for the RTL stick itself, depending on how things go, or potentially adding an LNA (Low Noise Amplifier) for the RTL stick to help it out a bit, just potential answers to help improve performance.
They work fine in my usage but, as I've noted in the past I don't even own a traditional physical scanner anymore, just these two RTL sticks for a few years now and I do all the monitoring I handle with just the two sticks, SDR#, SDR-Console/Radio, DSD+ and of course Unitrunker. The RTL sticks are never going to give you identical performance as an actual physical scanner will, but you can get pretty close and still have more than acceptable levels of performance overall.
Works for me. 
