It is Zen's IP that they have statically assigned to you. If there is a problem with routing to the IP then it is their problem to solve - if changing to another of their IPs fixed the issue then it is definitely their problem to resolve. It appears they are giving you the runaround.
Agreed, when ever I have spoken to Zen Support I have always had a good experience with them, seems the OP was unlucky and ended up with an idiot that had no clue.
While the user is responsible to what they use the IP for, if there is any issues then the ISP should all possible tests to resolve the issue and if changing the IP resolves the issue then great.
If not than change it back to the old one and look into other possible reasons what could be causing it.
If the supplied IP is assigned to a domain address then Zen could give out an additional IP temporally which they do tests.
TBH, I would try another Modem / Router, it might be that or just a routing issue, I know Zen has messed up with my brothers connection, when he was here in East London they had his connection routed up north and then back down to London, so his latency isn't that good
So Zen can and do mess up now and then as do other ISP's.