...the two problems we encountered with scrum (stuff never gets tested, no metrics to show when project will be complete) seem to exist just as much with Kanban ...

This is fairly simple to address, as your true problem is not Scrum or Kanban, but rather the assumption that a Scrum or Kanban task board in Jira is enough to give you the insight (metrics) you need.

You also need (a) a high level product backlog/roadmap that can be used for estimating and reporting completion and (b) a reliable test process, within your control.

When the product will be complete :

How close you are to completion can be monitored, estimated and reported by looking at the % of the user stories (or epics) completed in relation to the total number of user stories (or epics) in the original product requirements. Without a checklist of any kind there is no way you can estimate completion and/or total costs.

Never “done” because things don’t get tested :

The definition of done has to be in your control. Either hire a test manager to make sure it gets done and is in with your control, or remove the “externally tested” step from your board. Board metrics are only useful if they measure your performance in a process you control, so that you can predict future performance for tasks you control.

You sort of answered your own question when you said:

... we're not really doing scrum ...

An underlying assumption behind both the Scrum board and a Kanban board is that the tasks can/shall be completed by the team/resources using the board. A velocity is only a useful metric for estimation if can help predict the future performance of those same resources.

The Kanban metrics assume that the tasks are of a similar size, without much uncertainty, and helps you measure throughput. Again, knowing your throughput and using it to estimate completion is only useful if the metrics represent things in your control.