I'm new to Jira and cannot find any help, Google or otherwise, on simply making a Dashboard component which lists all Users and their most recent Work Log entry. Any thoughts?
I would take a look at the Jira tempo plugin, it will solve all your time tracking and recording issues. We also combined it with the worklog assistant, since not everyone likes to book hours, this will simplify it a lot.
List of recent work-items per project: https://tempoplugin.jira.com/wiki/display/TEMPO/List+View
Team time-sheets: https://tempoplugin.jira.com/wiki/display/TEMPO/Team+Timesheet
I would expect you can also add these list and views to your Jira Dashboards, although I never tried.
You can use the Jira Activity Stream gadget
Yes, Jira has a built-in gadget to do this. It is the Activity Stream gadget:
You can add this gadget to your Dashboard and select all the projects that you want to track. I find this gadget very convenient to track all Jira and Confluence activities as a stream in the dashboard.
However, please note that I am using it for Scrum. You will have to try this for Kanban to see whether it meets your needs.
Jira Activity stream has also a table view, which looks similar to what you requested:
To get that, Add Gadget to your Jira Dashboard and then use toolbar (seen on my screenshot) within the "Activity Stream" to switch to table view.