Acceptable notation? $\lesssim_{n} n^{-\beta}$ for constants NOT depending on $n$

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I am preparing a paper and found it convenient to write things like $$ |\text{Expression of a lot of variables}|\lesssim_{n} n^{-\beta} $$ when an inequality is true up to a multiplicative factor that does NOT depend on $n$. Unfortunately, so far I have ever only seen people use this notation in the opposite meaning that would interpret $n$ as the only thing that the constant depends on.

The reason I want to use the notation differently, is that otherwise I would have to use a lot more subscripts.

I do currently clearly state what I mean by my notation. Also the inequalities are almost always as easy as above such that no one could misinterpret them without intention (the above would mean $|\text{Expression}|=0$ for all $n>1$ if the constant did not depend on $\beta$).

I still wanted to ask if you think changing canonical notation like this is a good idea or would annoy people. Or maybe you haven't seen either notation and there is not even a canon I could break.