You can't be compelled to incriminate yourself, but your server provider can very much be compelled to give access to the server. And once the server is physically compromised the battle is lost, anyway, but in that case probably with a larger papertrail leading to you.
One expensive but possible option would be to build a server yourself with sufficient traps to shut off when it's tapered with. Then set it up with full disk encryption and put it in a shared rack.
Dedicated server (with standard hardware) can be prepared to be almost tamper-protected, for almost everything realistic attacks. Yes, it will be prone to freeze memory (physical freeze, with liquid nitrogen or liquid helium), but I don't think that it is what police in any country will do.
But as sibling comment mention, it can be seen as destroying of evidences in many jurisdictions :-(
What would be the benefit of being in a shared rack? Wouldn't the service provider still know which physical system is yours if you only rented a 1/2/3U space? (Or is there an advantage at a network layer?)
The shared part is only for pricing, since renting a full rack for a single server is a bit overkill :)
Going for a rack has the advantage that you own the hardware and can install the anti-tamper measures so that the server can't be turned against you. Anonymity wise, renting a server makes things a lot easier.
One expensive but possible option would be to build a server yourself with sufficient traps to shut off when it's tapered with. Then set it up with full disk encryption and put it in a shared rack.