Sharepoint 2016 On-Premise SPFx Alternatives

I'd be asking your architects what they define as "installing" something (as a Consultant I've made a career of challenging everything and frequently being told to wind my neck in). All modern development now takes place with client side code, so there's nothing that they need to install beyond the actual SharePoint 2016 supported updates. The SPFx elements themselves get deployed through the app catalogue, in the same way as Add-ins so if you're looking to do any type of portable development for SharePoint you're going to be adding items there. If you are able to persuade your architects, then jcgonzalezmartin is correct in pointing out that PnP will be your number 1 resource.

Is your Farm configured to support the Add-in model? If so you could explore SharePoint Hosted Add-ins or Provider Hosted Add-ins as they were the recommended way of developing for SharePoint 2013+.

If you still encounter resistance to that approach, you've always got Script Editor Web Parts which allow you to embed and reference JavaScript directly on the page.