I think you are absolutely right — the chances in the final round are significantly lower than what you experienced in the first and second round. In the first and second round, schools normally will have accepted a lot of people with similar profiles. So even if they don't reject you because of your background, they might end up rejecting you because they have already accepted similar profiles in the first two rounds.
So I think the right thing to do — if you are an international, and this is advice that I give to all internationals where you need a visa from the country of the school you are planning to attend, and you already know that they will have picked up people of similar profiles from your demographic — then I would wait for a year, retake my GMAT, get the right GMAT score without pressure, and then apply in Round 1. I would not recommend doing a hasty application and getting rejected — that will also have a negative impact on your chances of getting into these programs in Round 1 next year. So given that the number of programs that you are keen on applying to are very limited, like three to four, do not waste your chances with them by taking a hasty shot. Take it easy, work on your GMAT, and apply with the right score in the first round.
I want to tell you one thing from personal experience — once you start your program, it will become old news in three to four months. You might just regret later saying, "You know what, why did I not give it my best shot?" Because getting into a top school — getting into an MBA program or MS program or Masters in Finance program — that news becomes old in three to four months, and then you start thinking, "Hey, I could have gone to a better school. Why did I not try? Why did I rush through all of this?" So if you are doing okay at your job right now, and if you think you can afford to wait for one more year — which I am assuming most people can — then just wait and apply next year.
Of course, if I knew more about your work experience and what it is that you do, I could give a slightly more specific answer. But knowing what I know now, I would not recommend internationals applying to any of the business schools in the fourth round. I have been doing this for almost two decades now, and the kind of results that we have seen, the kind of scholarships we have seen — we have never done Round 3 or Round 4. Right after Round 2, we start telling people to come in the Round 1s of next year. The chances go up significantly.
The only time I have done Round 3 or Round 4 is when somebody had a very different, exceptional profile and I knew that this is the kind of demographic that the school would definitely want — or if somebody had a genuinely urgent situation, like they had to be in that program in that country this year because of some very personal reasons. That made the application feel like an emergency even though it was not one. But for any such personal reason, if they absolutely had to go — those are the only cases. Otherwise, I have always recommended people to apply in Round 1 or Round 2. Round 3 and Round 4 are not meant for internationals. They are not favoured by the schools for internationals, although schools officially don't say this because they also want to maximise the number of applications coming in. But I think it is only Round 1 and Round 2 that people should be looking at.