Looking at that code from moto-cms, it could be easily replicated in Dreamweaver. What I am seeing is Bootstrap v4.1 ( https://getbootstrap.com/docs/4.1/getting-started/introduction/ ), so if you have the latest version of DW you can likely build this out entirely and just remove the moto classes as the bootstrap classes are still separate.
I think what you are failing to see is that you are not really changing anything by doing what you propose and you would technically still be what you call a hybrid setup. DW templates are basically less efficient includes then doing includes server-side like through a CMS. So basically with a CMS, you have different regions (ie: header, footer, etc.) and then they give you an editor to edit the main content of the page. When you edit in your CMS, you are only editing either the content of the page, or the component (header/footer for example). When you use a DW template, if you make an edit to a component like a header or footer, you are making that change to every page on your site requiring your to modify and re-upload every single page that you are working on. For a small, personal site, this can work. But with a larger site, this becomes very cumbersome and time consuming to be able to reasonably maintain.
I am by no means an expert of Moto CMS, but work in many different CMS platforms and other automation platforms that operate like a CMS, and I suspect is that you have 2 templates in your Moto platform and the subpages are using a different template then your home. You should be able to switch everything to a single template if you want (or define multiple templates/themes/etc), but for that you might need an expert/partner in the MotoCMS world to implement. And also because your site is already based on Bootstrap which is a very popular framework, it would be easier to move your theme/template to another CMS platform, but as I said, depending on what you choose to go with, could mean a change in your web hosting provider depending on technologies you want to use.
Having done many of these projects before, I would not recommend using DW as a WYSIWYG editor because it's just not reliable anymore for that purpose and because of how frameworks like Bootstrap work. There are implications for mobile and other devices that need to be taken into consideration for the page to be responsive that makes it better to separate the code from the content through the use of a CMS especially for business sites.
What is your biggest complaint about moto cms? Is it the interface, the support? What limitations are you facing? I think based on those types of responses we can gauge as to what type of CMS may be best suited for your needs or to overcome your challenges.
After considerable input from the community, and my own research I am leaning towards a CMS solution. But not before verifying Cart32 forms will work within a CMS site? As I I don't know of any other form based shopping cart with the flexibility provided by Cart32.