I htink your following statement is incorrect. 'For example, an SVD that extracts 3 topics will yield different matrices compared to an SVD that extracts 4 topics.'.

Although this statement holds for most other topic modeling algorithms, it does not hold for LSA. LSA calculates the singular value decomposition of the document term matrix and returns topics based on the highest singular values. Regardless of the number of topics chosen, the decomposition will be the same. Hence, the topics will not change if you change the number of topics to find.