I agree with everything adventure_rn has said.
As an ER nurse, I would never run anything, compatible or not, with cardizem let alone insulin!
Even if technically compatible, my hospital has policies against running certain IV meds together, and both insulin and cardizem are not to be run with other drips, so you should check your hospital’s policies first.
Finally, I don’t see how an ICU patient can get by with only one IV. IMO, and standard practice at my hospital, is for all ICU patients to have at least one IV that is not in continuous use (running NS would be the obvious exception) when they have a continuous drip(s) running so that emergency meds, scheduled IVPs, or PRNs can be pushed without disturbing the drips and running into the same complications that adventure_rn described.