I've installed haveged in the VPS, but it's made no difference.
running
# cat /proc/sys/kernel/random/entropy_avail
gives values hovering around 200-400 most of the time. (much lower than the 1000 or so I expect with the default config)
And it looks like it's haveged failing to run.
Indeed your google links (thanks) suggest that you can't add entropy from a container environment
I'll see if I can get the host entropy increased
Good luck! I'm pretty sure that is your 'hang'-up. 
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OK. It looks like you are indeed correct
Running
# logstash --help
takes around 10 mins to run - but it does run eventually. Whether or not I can get the entropy levels suitably increased we shall see, but it does appear to be the problem - and hence not a problem with logstash. Many thanks everyone.
Thanks for the update. I'm unsure how much work has been put into testing
containerization of Logstash.