"In conclusion" is common, while "by way of conclusion" is quite formal. But what does "by way of conclusion" truly mean that differs from "in conclusion"?
When you consider other situations where "by way of" might typically be used -- for instance
By way of food, there was nothing in the fridge except a long-abandoned can of mouldy beans and a blackened banana
By way of reading material, the owner of the yacht had furnished himself with all 233 of Jeffrey Archer's finest novels
-- the expression seems to mean pretty much the same thing as "in terms of". Accordingly, by way of conclusion means roughly in terms of (a) conclusion, which in turn doesn't seem very different from in conclusion.
To my (American) ear, "by way of conclusion" means: "This is what I am offering as a conclusion". It may imply that this is not a real conclusion (in the technical sense of "given the arguments I have cited, I conclude that…). It may not be a "conclusion" at all, e.g. "By way of conclusion, let me mention a funny story I came across recently…".
When I as a reader encounter the phrase "in conclusion", I have every right to expect that the author will present a conclusion to, or at least a summing up of, the arguments and ideas they have presented in the article.
I was just wondering this very question myself! I think that "By way of conclusion, I will summarize my main arguments" means "As my conclusion I will summarize my main arguments."
But "In conclusion, I will summarize my main arguments" means, "Here is how I will conclude: by summarizing my main arguments."
The difference is subtle, but I think the first but not the second suggests that there are other good ways (perhaps better ones) of concluding than by giving a summary, and instead of concluding by doing one of those, I will conclude by giving a summary of my main arguments. But the second one just says, This is what I'm going to do:
My real question, though, was how this meaning could be derived from the more general meaning of "By way of...."