Full memory encryption is out of the experimental stage, but I can't name any hosting services using it yet. It's supported as an operating mode for AMD Epyc and Ryzen Pro - https://developer.amd.com/amd-secure-memory-encryption-sme-amd-secure-encrypted-virtualization-sev/ - so we'll probably see it available soon.
The intent is specifically to prevent a rogue admin from stealing the data from client VM operating in his cloud infrastructure.
The encryption used is AES in tweaked ECB mode, lacking authentication, so it's not a secure system. Specific attacks on it have been proposed: https://arxiv.org/ftp/arxiv/papers/1712/1712.05090.pdf
Homomorphic encryption is very far from being practical for remote hosting - if you can afford the overhead, you can run it on a Raspberry. The interest in it is currently aimed at privacy-preserving public records for voting and transactions. Homomorphic encryption really comes into its own in a blockchain context, so we're likely to see more applications.
It's possible to design a system that protects the data even with compromised hardware. But the x86 architecture wasn't designed with attacks in mind, and it's proving difficult to work around its implicit trust. Since you're asking about current ways, the most straightforward way to get provable security is building an ASIC that enforces authenticated encryption ("There is only one mode of operation, and that is secure") and only accepts signed commands and data.
However, even current insecure memory encryption (strong cipher, weak mode) does make it more difficult to surreptitiously steal your the data. It won't do for classified or highly valuable information, which is worth risking exposure for, but, combined with active security measures and oversight, can make opportunistic data mining a lot less likely.