No offense, but I'd get a different case. Those HP "gaming" cases are basically sh**. If that's not an option, then I'm not sure you can upgrade the fan situation because I'm not seeing that there are additional fan locations on that case, so unless there IS room and you are willing to do some rather involved modifications, or unless there ARE additional fan locations that do not have fans installed currently, a different case with better internal arrangement and additional fan locations might be a much better ide.
Forget the Grizzly grease, it's not particularly exceptional. The Thermal grizzly Kryonaut and Conductnaut are a different story but unnecessary in this case and rather more difficult to apply correctly. I would stick with Arctic Silver 5, Noctua NT-H1, Arctic MX-4, Cryorig Cryopaste, Prolimatech PK-2 (Not PK-3, which is a nano-diamond compound and not as easy to get installed correctly), or any of the bundled compounds that come with most of the major coolers like Noctua, Cryorig, Phanteks, Scythe, Deepcool, Cooler Master or other coolers.
The thermal paste that comes with the Cryorig H7 is very good, and I would just probably use that. Otherwise, the Noctua NT-H1 or Arctic Silver 5 are my usual go to thermal compounds with MX-4 as a usual version for less demanding, lower mounting pressure option.
As a test, I would run your system with the side panel off. If your temps drop significantly with it off, then I'd definitely consider a different case or some way to add case fans. If it doesn't, then it is likely the CPU cooler is not mounted properly or is simply not up to the task.