How can I avoid overuse of words like "however" and "therefore" in academic writing?

Let me suggest an alternate view. This is in regard to writing proofs and other very technical things. You want, above all, for your intent to be clear. It may be that "however" and "therefore" are the best available words and that they clearly express the flow of the argument.

After all, if you were writing the proof purely symbolically you would "overuse" certain logic symbols in order to be exact.

And, don't let "fancy words" get in the way of your readers deep dive into the ideas themselves. Sometimes the most obvious word is the one that is most quickly understood to express your intent. This might be especially important for those who know your subject, but are not native speakers of your language.

OTOH, I haven't actually seen your prose. If an editor or reviewer objects, then you can change it to suit, of course.

It sounds to me like you're actually doing everything that you need to do already.

In fact, when you are initially writing a paper, I would suggest that you not worry about it at all. Write things as they come out most quickly and naturally, focusing only on conveying the substance of your argumentation.

Only at the very end, when you are polishing before submission, is it worth worrying about the wording. At that point, you can read the paper out loud to yourself and see if you start feeling repetitions or stumbling over sentence structure. Reading out loud is valuable because it slows you down and forces you to really hear what you have written. If your words feel uncomfortable when you read them out loud, then fix them just like you are doing already: deleting when you can, and substituting synonyms when you can't.

Aggressive Pruning

I agree with other answers that your repetition of however and therefore might not be a problem in this context. However, I would like to point out another option. These words are usually included as signposts for the reader, but do not change the meaning of the text. Therefore, I suggest omitting them. For example,

I agree with other answers that your repetition of however and therefore might not be a problem in this context. I would like to point out another option. These words are usually included as signposts for the reader, but do not change the meaning of the text. I suggest omitting them.

Just try removing the offending words in each sentence where you feel it might be getting repetitive. In most cases, you'll find you can remove "therefore" or "however" without impacting the argument. If the transition of ideas is jarring, leave the words in.

You mention that you remove instances like this already, but you may not be aggressive enough. In your question, you state

Often, I can just delete some of the "however" or replace "therefore" with words like "consequently". I can also sometimes change the wording to use "then", "so", or "but". However (see I can't even help myself), I feel compelled to use words like "however" to help with flow.

To me, the "however" in the last sentence is optional. You add it to emphasize contradiction with the previous statement. You could replace with

Unfortunately, I still feel compelled to use words like "however" to help with flow.

I would suggest an exercise where you remove all "however"s and "therefore"s and then wait an hour or so. After the wait, re-read your text and re-add the words where necessary. The time gap will give you time to forget where the words originally appeared and allow you to read with a fresh perspective. This should help with more aggressive pruning.

Rephrasing

As regards to synonyms, sometimes rephrasing the sentence works better than rarely used synonyms like "ergo". For example,

I agree with other answers that your repetition of however and therefore might not be a problem in this context. I would like to point out another alternative. These words are usually included as signposts for the reader, but do not change the meaning of the text. When this is the case, I suggest omitting them.

Rephrasing can also emphasize contradiction and support in the same way that "however" and "therefore" do. For rephrasing, the same exercise as above can help, but I also find proof-readers invaluable. They often find ways of stating the same thing more succinctly and elegantly because they have a fresh approach to the text.