As a noob to RF, one thing you may not be aware of is that all RF is heavily regulated by governments, including products that use RF, and those of us that work within those regulations are trained to comply or perhaps feel morally obligated to work within the law. The reason that RF is heavily regulated is simply because nothing RF would work if there was no traffic cop to keep it all in order. This is something to keep in mind as we offer advice.
It is very likely that your shot clocks use wireless that is what is called "license-free", meaning the user doesn't need a license to operate them. There is an understanding, a contract if you will, between the manufacturer and the government (of most countries) that as long as the manufacturer builds their products to meet certain rules, then they are allowed to sell them to anyone as license-free. This is really nice and convenient, but this freedom from licensing comes with a price, and that is that the technical limits for such devices don't allow them much range. These technical limits include that they cannot transmit more than a certain, relatively small, amount of power, that they cannot be modified by the user, that they cannot be capable of changing-out antennas, and, the biggest restriction of all, they must suck it up when they receive interference. By this I mean that they have no protection under law from any other users of the radio spectrum. In the United States, the technical rules for license-free devices are called the Part 15 rules (as they are Part 15 of Title 47 of the Code of Federal Regulations) and so we call this kind of device a Part 15 device.
So much for the lecture, now about those shot clocks. Yes, if you have considerable RF circuit expertise, anything can be modified to improve link performance by adding better antennas, or by increasing transmitter power, but these things are not easy. One reason is because part 15 devices usually are not modular, and by this I mean that they don't make it easy to change antennas, or amplifiers, because they are not allowed to. And adding RF power is technically very tricky to do. Let's consider other ideas instead. The most powerful thing you can do is put some distance between your devices and the ones that are interfering with you, so first thing to do is identify where these interfering transmitters are. This is usually done by doing some RF direction-finding. Once you know where they are, the most useful thing you can do is move your shot clock equipment, or their equipment away or apart somehow. Putting some walls and floors between can be helpful too. The other options open to you are choosing channels or hopping sequences (if applicable) between you and the interferers so that everyone can get along without trouble. For example, sometimes it is possible for a frequency hopping device, which it sounds like your interferer is despite what you see on your analyzer, to be programmed to avoid certain channels. Perhaps, if your shot clocks are single channel devices they can be programmed to operate on these selected quiet channels?