Finnlights, from my experience and research have a few documented issues, which are interrelated to a degree. All are also worth your consideration in making your decision. All have presented on my rifle and have caused me to analyze the possible solutions, which may be of some assistance to you.
1. Light weight = surprisingly potent recoil relative to the calibre and of course that comes with the related complications. Here is where a 7mm is feeling like more than a 7mm, I know my .308 feels like more.
2. The recoil lug system and some peculiar hollow areas in the stock do not do their jobs as well as one might hope. This has been a reported cause of potential accuracy issues.
3. The fluted barrel heats up quickly and POI shifts can be significant with follow up shots.
How are they interrelated? And what does any of that have to do with a muzzle brake?
By many accounts, a McMillan stock has been able to remedy the recoil lug/stock hollow issues, which have caused many owners accuracy issues (I am ordering a McMillan for my Finnlight as soon as I decide on a few details). I have seen the stock remedied by altering the stock, but this may not assist with fit. When you consider a custom stock, you can order the stock to be the right fit and have a high quality, properly fitted recoil pad. This may assist in felt recoil. You also may be able to make some weight considerations. Finally, with and without the brake will shift your POI and in a rifle that can already shoot differently on shot 2,3 etc as the barrel quickly heats up, it adds another potential complication in the form of recalling which POI to expect at each point.
I would suggest trying a recoil pad first, as the one it comes with is a hockey puck. For me, this alone made the difference between discomfort after 5-10 shots and no problem shooting a box in a sitting, and my LOP is not ideal either. Measure the LOP to perhaps add the recoil pad with a preferred width in mind. The better the fit, the better your comfort. What is the weight of the rifle overall and the scope/ring setup? Perhaps adding some weight there could help also. A butt sleeve with extra rounds and a scope level could also be functionally relevant and add weight. Finally, the custom stock idea with custom LOP and maybe some ability to increase weight might be an idea.
I would at least consider those things before going for a brake. A 7mm may be able to be tamed to within your comfort zone with another change or changes. Brakes are loud for hunting and your companions. A brake may also do unnecessary damage to your own hearing over the years. They also shift POI. Last resort in my books. Lastly, revisiting shooting fundamentals and recoil management may round out a complete approach.
Good luck!