Here is my best plan so far:
The middle step is the hardest part. A centralized exchange would see someone buying XMR as suspicious, and might indefinitely freeze the transaction until identity verification (KYC) is provided. Pretty much, the centralized exchange would already probably know where cryptocurrency to be converted to XMR is coming from. Even though they won't know where I would use the XMR, the fact that they would know that I am using XMR would be privacy-intrusive enough for me. If the transaction freeze happens, I would simply forego my deposit and forget about the transaction, but it does not mean that they would forget who I likely am, and that I attempted to convert my cryptocurrency to XMR.
Testing the conversion of $1 worth of cryptocurrency to XMR might succeed without being forced to undergo indentity verification, but the next conversion of $100 or even $10 might not succeed.
Thank you for reading.