How would I display a CMS Theme Demo within a Laravel site like themeforest?

Is your question about a portfolio displaying your own work? Or is it about a build application that you want to demo?

The easiest solution is most of the time running the same application on a different URL with dummy data.This way you can do with the demo what ever you want.

Its about a portfolio displaying my work. A different URL or subdomain makes sense.

You could create screen captures, either putting them in a carousel OR display them on one page. You could allow them to click thru to the showcase websites with a preset username/password.

Imho, I think it could be a ton of work to replicate the website within your base CMS site, and I don't see anything to be gained to do this. This also keeps the maintenance down as you don't need to maintain the main site and the one you jiggered to work on your showcase site. You only have to redo the screen captures this way.