How can I counteract the meaning of "only" changing due to verb modifier?

As with any adverb, the precise position of the adverb makes a difference: before/after the verb/verb phrase and before/after the clause/sentence.

As with most words, only has a variety of shades of meaning, and we see that in your sentence:

I only strive towards success.

First there is one you mention: the only thing I strive for is success. Then there is the broader sense: the only thing I do is strive for success. Then there is an apologetic sense: I was only doing my best to succeed. Then there is an alternation sense: Only I wasn't trying to fail but to succeed.

Generally language is ambiguous, and the longer and more complex the sentence the more ambiguous it tends to be. Sometimes the best way to clarify is by breaking the sentence up, or by following with a disambiguating phrase or sentence, as you have explored. Sometimes you can move the adverb or change the tense to clarify. Often you don't need to do anything because it is clear in context.

Consider these variants (not all of which sound natural with the verb phrase used) - you can match them against the four shades of meaning above (exercise for the reader, figure out the permutation and the logic):

1. Only I strive towards success.
2. I only strive towards success.
3. I strive only towards success.
4. I strive towards success only.

So the answer to the question is "move it": move the "only" to the place that gives the intended meaning!

I'm not sure I see any difference between the meanings of

• I only strive towards success.
• I only strive. This striving is towards success.

But, since only is a quantifier with a stressed focus element, if you want to make strive the focus, just stress it. Normally one would stress success as the focus of only, and stressing the last word in a sentence is a natural pattern, so that's almost the automatic interpretation.

BTW, by stress, I mean say it LOUDer (the first syllable of louder is stressed). English has several levels of stress, and most words have a stressed syllable; further, every sentence has words that are stressed or unstressed. This is why we're not often confused about what only means in speech; that only happens in writing, which doesn't represent stress.

"I only strive towards success." -- ambiguous.

We mean
"(I only strive) (towards success)."

So it would be,
"I only strive, towards success." -- the comma removes all doubt, and serves just that purpose, being otherwise redundant.