You can define unique capabilities for a particular post type. A user without these capabilities cannot do anything related to the post type, not even admin users. They too will need these capabilities assigned. Those with the capabilities can do whatever that capability allows, even if they are only a subscriber role otherwise. If the current admin screens for the post type meet your needs, then managing capabilities is the way to go.
“the Submissions screen is a post-type, and the edit screen is a post edit screen.”
Not quite. The submission and edit screens might be the same thing. What is allowed is determined by capabilities of the user. The post type would be tanks in your example. Each tank’s data could be stored in post meta. Every tank is a different post of that type. It’s up to you how your submissions and edits are displayed and handled. You could use the current admin forms if they meet your needs. It doesn’t sound like they do from your description. In particular, post meta is not handled very well by WP by default. This could be cured by adding a custom meta box to the post/tank edit screen and/or customizing the post list table columns.
Depending on the user experience you would want, the admin forms might leave much to be desired. If nothing else, the WP back end is not themed anything close to your front end. For the best UX, you may wish to develop front end forms to handle tank post types. A UI built on a custom page template that is styled to be consistent with your theme is easily attainable if you are capable of building such a thing outside of WP. Custom page templates are little different. Perhaps where and how the data is stored and retrieved is different, but displaying the data and building the UI would be identical. I personally would go this custom page template route.
You could still use custom capabilities to manage who does what with the data, and the back end forms could still be used if anyone cared to. Why would they if an awesome front end UI is available? ??