That's a neat looking little discone!
I've tried indoor yagi's that were intended for outdoor use.
Some have luck but mine made things worse due to reflections from metal cabinets and the like.
You probably could try building a simple yagi and see what it does.
Something simple and cheap. It may be worth a shot.
Yagi's are actually pretty simple and for testing purposes, it does not need to be pretty!
I was in the same boat as you living in the apartment I still live in.
One day came where I had a valid reason to have an antenna on the roof. I live on the top floor. I was surprised when the apartment manager gave me a key for the roof hatch and written permission to install what I needed.
They still allow it to this day and I now have multiple antennas on the rooftop. I do try and keep them to a limit though as I don't want to push my luck.
I first needed to get a signal from a 902 to 928 lightning detection transmitter located at work about 1.2 miles line of site.
I bought a yagi for that band and it worked fantastic.
Since, I've put up single or multiband antennas of the omni or directional type as well as a loop and several long wires for HF stuff.
I keep the wiring nice and tidy and they are happy. I do consider myself very lucky they allowed it but the main reason for it was a true valid reason and still is to this day. I've had various antennas above my apartment for over 20 years now.
I do tend to remove one though if I'm installing something new to keep the count down.
Luckily they are not that visible from the street so that helps as others here do not really notice them.
Only one is used for transmitting back into my business repeaters at work but I only need a watt or two so no interference complaints.
I'd experiment with building a simple yagi if you have the time and knowledge to try it. If you have a window facing one of the towers giving you problems, that would be the window to aim the yagi through.
I once had a 20 something element yagi for 900 MHz. made for amateur radio that I bought up at Dayton a long time ago. I had it hanging in my bedroom aiming out the window at the site I was after. I had multiple hooks in the ceiling so I could change the aim a few degrees.
It did actually work but not near as well as I really wanted.
The wife did not care for it though!
I changed the reflectors with a pair from a TV antenna and that also helped. It was shortly after that when I was allowed to install an antenna on the roof. I never did install that huge yagi on the roof as it was almost 10 feet long with all the elements it had!
I ended up using a 12 element Maxrad yagi that was made for 800 MHz but it also worked well for the low power 900 MHz signal from the 900 MHz freeband (ISM Band) radio signal I needed. With luck, the aim to work was also inline with the aim I needed for the cities new 800 MHz trunked system.
Some people use wood broomstick for a homemade yagi and some use PVC pipe. Either should work for a crude antenna test.
My apartment itself is covered in Stucco which is applied to a wire mesh. It's almost like I live in a Faraday cage so indoor antennas did not work unless I had a window to aim through.
I've only used indoor antennas for really strong signals the past 20 years or so.
One thing about the Stucco walls is that it also helps keep the neighbors EMI/RFI noise out!
You may get by with a tiny 3 element yagi with the signal strength you are showing.
You just need to try and null out all towers except the strongest one it looks like.
I'm not familiar with the antenna in your link from ScannerMaster.
It seems pricey though so I'd try and build something before investing that much money in something that may not work.
An UHF yagi style TV antenna may also work and you can usually find something cheap at places like best buy or even some of the big box hardware stores.
Try and find a UHF only model usually sold as an HDTV antenna that is not amplified. The amplifiers in those usually add more noise than any gain they offer and if you can find one for UHF only, it should keep the size down. If it does not work, you should be able to return it.
That would be easier than building one!
The UHF TV band starts just above the 800 MHz public safety band but should still work for the 800 MHz public safety band.
You will have a slight mismatch in impedance from 75 ohm at the antenna to the 50 ohms a scanner is looking for but for reception only, that should not matter. You can even use quad shield 75 ohm coax as it has very low loss at 800 MHz and is small diameter compared to something like LMR-400. Then you only need one adapter at the radio end to convert from an F connector back to a BNC.
If you have a camera tripod, you can mount it on top of that and see what happens.
If it works well, then build something that fits better indoors.
Wilson also makes some small non amplified cell phone signal booster antennas that are very small and contain a tiny yagi inside the weatherproof housing. They sell one that covers down to the 700 MHz band on up. The whole thing is only about a foot long and has an N connector output for 50 ohms. They don't really offer much gain but the directional properties are very good. Here's a link for one that looks like the one I have but mine does not offer such a high freq range. Hopefully the link will open.
https://www.wilsonamplifiers.com/wi...0ohm-314411/?gclid=CI_QuomAz84CFZU1aQodUbUP_Q
They are small and don't really offer any gain but do have decent directional properties and do help null out signals off to the side that may be causing simulcast problems.
You can find them cheaper and don't let the claimed gain fool you. They really don't offer that gain but I don't think you really need any gain, you just need to null out the signals from the other towers on your simulcast system.