Binance is the best place to convert such big amount without KYC because other p2p platforms will have liquidity issues which may take too longer for the trades to get completed.
If the exchange has a KYC program already in place that means they can force anyone at any time to comply with it and block their accounts with their funds until they submit their documents. It is not wise to use centralized exchanges if you are looking for privacy and don't like to give up your documents to strangers!
I would also advise against using stablecoins for storage under any circumstances. They are highly risky even if it doesn't look like it because they are all centralized altcoins.