All right let’s get back to the core of everything and simplify things here. It sounds like you’re making this way more complicated than it should be.
In this theme, there is simply a text field that holds your logo image URL. Whatever image URL you put into that text box is what is going to show on your site, simple as that.
In WordPress when you use the scale feature, what it does is create a NEW image URL for that new size, and it will leave the original size there on your server in case you wanted to revert back to it (I think that’s why anyway).
I tested more. If I paste the reduced image (the one for the logo) on a page it is scales fine.
Show me a link to this attachment page with your logo the size you want in the body of the page and I will tell you the URL is that you should be putting into the option on your theme options page.