Normally I don't have much faith in third party apps either unless I am personally familiar with them so I do understand some consumer facing staff and even some techs might not take your allegations seriously. However, I was investigating a similar issue with a MBPro and saw someone use Intel Power Gadget so I tried it out. While I don't like the app itself at least it provided me with the necessary information about the throttled CPU (I'm not aware of any other app or method to do this on macOS). I also verified issues using Linux as well. This app is after all made by Intel who created the CPU in this laptop so the tech really should at least take a look at your findings.
Was this an Apple Store or an AASP?
You may want to try contacting an AASP (or another one if you have more than one AASP in your area). You just need to speak with someone who understands the technical aspect of what you are describing since many people at the front desk taking in computers may not have the necessary technical knowledge. Apple's method of repair is to just follow a list of steps to replace major components. Apple does not train techs to think for themselves or to understand the lower level technical details. Of course an Apple Store or AASP may have a tech(s) with that knowledge or skill, but many do not so finding that one tech is essential.
Maybe another way you can convince them that there is a problem is by running a stress test on the laptop and use Activity Monitor to show them the CPU cores are at 100% utilization yet the CPU isn't hot (just feel the keyboard & bottom case and notice the fan is not running at high speed). Do this first with WiFi disabled so everything is cool. Then enable WiFi and have them see the fan start running faster and the CPU getting hotter. At least this way they can use Apple's own software (Activity Monitor) and their own senses (ears for hearing the fan, skin for sensing temperature of the top case/keyboard & bottom case). I don't normally use the Intel Power Gadget since it is hard to install due to Gatekeeper and I just use this method to determine the CPU is being throttled (or I will use Linux to confirm). Ask them why the CPU is not getting hot when the fan isn't running at high speed when all the CPU cores are maxed out. The CPU cannot be running at full speed without creating heat. It is impossible so it should clearly show a tech there is a problem especially when you toggle the WiFi on and it gets hot within minutes. To maximize the effectiveness of this demonstration perform a clean install of macOS by first erasing the drive before you reinstall macOS. Do not install any apps or restore from a backup.
A good way to stress the system to heat it up very quickly is by running "mprime". Personally I like to use the command line version since I've had some trouble running the GUI version on some systems. If you've never used "mprime" you just drag & drop the "mprime" executable to the Terminal window and press the "Return" key to execute it. The first time you run "mprime" you answer "No" when asked about "Joining Gimps" so you access the stress testing portion of the utility. Accept the defaults by pressing the "Return" key except for the question about which stress test to run. The tests are numbered 1 to 3 (or sometimes 4). You want to select the test which mentions "maximum power/heat".
Any really good hardware tech should be familiar with "mprime" or its Windows equivalent "Prime95" since "Prime95" has been around 20+ years and is a staple for testing custom built systems and overclocked systems for stability and proper system cooling. Even if they are not familiar with "mprime" it shouldn't matter since Activity Monitor can show the CPU at 100% utilization on each core which should make the CPU extremely hot and cause the fan to run at high speed. You should experiment with this at home to see how quickly the CPU heats up using this stress test so you can put on the best show when presenting this to the repair shop.
Good luck. Unfortunately I think you may need all the luck you can get.
