Comma usage: Sentence starting with "But", sentential adverb, and followed by "when"

Question

I have a sentence structured as follows in a scientific text.

But, in particular, when doing A, the system cannot do B.

I think all commas are formally required. However, for "But" in particular, I am always urged to omit the trailing comma, since doing a reading pause feels really awkward. The same holds for "But in particular" and to some extent for "But in particular when".

Question: Is there any rule that would allow omitting one of the two commas in the first part of the given sentence in a scientific text?

Edit: Here is an alternative summary of text, incl. the sentence before the "But".

The previous solution avoids to make any assumptions on effect X. But, in particular, when doing A for objects Y1 and Y2, this may cause effect B.

Based on the discussion, I now rewrote this as follows.

The previous solution avoids to make any assumptions on effect X. This may cause effect B, in particular when doing A for objects Y1 and Y2.

I did not move the "in particular" to the end of the sentence, to better emphasize the whole when clause, rather than only the "objects Y1 and Y2".

Answer 1

This is not an answer to the original question about any punctuation rules. However, given the comments to the question, the conclusion for the underlying problem may be the following.

If you are unhappy with unhelpful commas, your sentences may be stylistically weak and probably need to be rephrased.

Answer 2

This is really a style issue. As such, you can do what you feel is best or be consistent with a reputable style guide

The Chicago Manual of Style discourages the use of commas following and or but even if these words start a sentence or act adverbially.

As for your last example, I think you need some break for clarity, but I would use an em-dash rather than a comma.