Very curious why you want to do this?
It's certainly not for money laundering related reasons like you've mentioned above.
You can just start your own pool and just rent some hash power on Nicehash and point it there, eventually you will find a few blocks. Very curious why you want to do this?
That is very expensive and time consuming. What I'm doing here is basically paying extra money to the miner for what they are doing anyways.
The premium for Nicehash ETH hashrate is not that large at the moment, how is it more expensive. How much more premium are you going to pay some miner to mine ETH for you.
Why do you need specific blocks, the mined blocks will be sent to the miners address and they will send those ETH blocks to you, how is this any different from buying ETH from an exchange? I don't understand what you are trying to accomplish here.
If you explain what your specific plan is, we can help you out to find the cheapest route to acquire ETH.