Helio, I like the idea of *tweaking*. I just think when some start tweaking, the model may have more issues than commonly reported
Yes, that's a possibility with any theory. Einstein "tweaked" Newton's gravity model, but even this didn't really change it as long as gravity gradients and incredible speeds don't affect the decimal points needed.
But the BBT is a story of remarkable success. I'm not sure what other predictions are being tested, but so far, so good.
This isn't true for Inflation theory since it is extremely difficult to test the predictions it makes. It, or something like it, is needed to tweak the early version of the BBT. But the fact that something is needed doesn't falsify the theory, but weakens it. So, the Inflation theory made it that much stronger even if the first model requires tweaking. If another model, however, could compete with BBT, then that could weaken it perhaps.