It's hard to get around the cold hard fact that a 400ms round trip time means that nothing that requires talking to the server can happen in less than 400ms, which is nearly half a second. (Consider that Einstein, himself, is imposing at least 50ms of that latency upon you from the grave.)
How large/complex are these java graphics? The NoMachine NX client has controls for both RAM and on-disk caches. The RAM cache is configurable from 4MB to 128M. And the on-disk cache is configurable from 0MB to 512MB. Depending upon the exact workload, large caches may help. But I'm not sure how to set that in x2go. (What does the '16m' in '16m-jpeg' actually mean, I wonder? 16m RAM cache? Something else?)
Regarding trying out 'LAN', I can tell you right now that's going to perform *extremely* badly. I'd have a lot more hope for 'WAN'. My best *guess* is that ADSL *may* be your best bet. But do try everything and see what works best.
-Steve