Based upon what you've written, it's a pretty cut and dried case, and you'll need to apply in Zim.
There may be an avenue based upon the recent election and Zim's subsequent expulsion from the Commonwealth, but I am seeing full charter flights of removals every month and doubt you could have a case. Do you think you have an Article 8?
This particular forum doesn't have expertise in visa-national applications, but there's other boards that do. In all events, my read is that you have a very normal, cut and dried case of needing to make an entry clearance application.
Although family is supposedly not affected by the deadline in 2 weeks, your app would be less complicated if you filed between now and then.