Hey. If you are not reusing addresses, there is no way that anyone will know that you own the addresses that you send bitcoin into.
Use a new address for every bitcoin transfer on your trezor (as far as i know, trezor does generate new address for every time when you are receiving BTC).
If you are paranoid about your funds, you can always use bitcoin mixers or swap funds to monero, and monero back to bitcoin (or just use the Dash method that you were talking about).
If you want to keep your transactions private, you cannot post any addresses that you use for the transfers that you wish to keep private.
If you wish to get easy to use bitcoin mixing to keep it simple, i can recommend
Bitmix.biz. If you wish to use their tor service,
Then here is their onion.
Best of luck securing your transactions, and if you got any more questions feel free to PM or quote me here.