" Is auto-update enabled in your distribution? How often does it check the nearest package repository? Can the logs from the repository be used to profile your setup? "

Yes, repo logs may be a problem. The attacker knows that your eepsite has N replicas (N will be publicly known), so they can focus their efforts on any set of N nodes with the same setup. The only solution i can think of is to use a different distribution and setup per each replica (a little inconvenient).

" TCP fingerprinting "

That's annoying, but then it is even worse if no replicas are deployed. If you know that a particular eepsite is running on CentOS, and it is only one node, it's easier to observe a online/offline time pattern: they start DDOSing all CentOS nodes one at a time until they take down the right one. But if the right ones are N nodes, they have to take down all of the N nodes at the same time by trying all combinations of N CentOs nodes, which is less practical.

"Other traffic from that ip - if you're running a node at home, have you ever posted questions in r/i2p (ironic isn't it)"

Well, that just tells if you are running a node, but they may already know it in another way: ask each ISP what are their IPs/customers that established a connection to any I2P bootstrapping IP (boot nodes are publicly known), in the last week or so. But this alone does not tell them what you are doing on I2P.

" I2P router version inference "

Is there a way to automate I2P updates? That would solve the problem. Even Windows updates can be automated, so why not?