Team, I use Amp for several instances of Minecraft and Ark. The mechanism it uses right now is not delta-based, so each backup is very expensive, and it limits the granularity possible with its' backup mechanism.
In the past, when I wasn't using Amp to run those servers, I manually set up Minecraft and Ark servers on the same Linux instances and made use of rdiff-backup to perform my backups. (http://www.nongnu.org/rdiff-backup/) I could back up hourly, daily, weekly and monthly.. and it was so efficient that I would literally be able to have 23 hourlies, 6 dailies, 3 weeklies and 6 monthly backups in the space it took to store about 3-4 single backups without delta differencing.
I completely understand that my use case was not a 24x7 in use server with 2,000 concurrent players.. (more like 3 players logging in for several hours a day at different times) But there should still be significant space savings with improved granularity if you adopt a differencing algorithm like rdiff-sync. (not to mention you have the benefit of easily placing backups on any kind of storage, even remotely) And the restoration mechanism is excellent.
I pointed out that tool above specifically because it's open source and free. I'll probably move to it, even when I'm using Amp, since the mechanism built into Amp is so expensive for resources.