Hey,
This forum is huge, which is why I reply so late.
I do not believe that you need to do log analysis to get better. Your way of getting better might not be the quickest, but still there is no reason why it would not work.
I tried to read your previous posts as well to understand your gaming problems better, but I am not sure I still have a good understanding as such things are pretty complex. From what I understand you could still keep your way of getting better, using intuition and brute force, as long as you understand that you need different approaches for different boards. You can see the whole thing of dominion as having many different subgames. You certainly do so anyway, like rushes engines slog etc. The thing is that you should categorize the boards to many more subcases, like tournament, inheritance, or wherever you seem to play weak. You should consider it a different area were you will have to get another model of intuition and not use the previous ones.
Also, once your intuition tells you what to do on a board, stop and ask your self, how all the other cards could interact with what you want to do and if there is a trick to make it quicker. Eventually this is another subgame where you can develop your intuition.
I am not a very intuitive dominion player my self, but I do understand how it works and cannot really see it being that limited as you seem to think at the moment. Yes it does take work to build many different models, but I do not think there is any shortcut to help you there.