One tactic you can take for “formal” styles is that you can write formally but then restate the same thing informally. This can both take on the tone that you wanted to have but also put things in a way that might be more easily apprehended (or, understood!).
For instance, here’s a sentence I might write:
Systemic-functional linguistics (SFL) is built on the assumption that language is a social semiotic system. SFL is about what a language can do in a given context, rather than what it “is,” which makes it a good partner for rhetoric.
The first sentence has several words derived from French (systemic, system, social), Latin (functional, linguistics), and Greek (semiotic). It does have some core, too, (built, on, the, that, is, a ), but only “built” makes much more central meaning whereas “on,” “the,” “that,” “is,” and “a” all fill roles to connect the sentence together.
The second sentence restates the first, but uses much more core language to explain further but also amplify to emphasize what the point is. Here, core words like “about,” “what,” “it,” “‘is,'” “which,” “makes,” “good,” “can,” and “do” play a large role in the point of this sentence: this theory of language is about how people use language rather than what language is and thus helpful theory for studying rhetoric. There is Latin (“context”), French (“partner”, “language”), and Greek (“rhetoric”) here, but they play more minor roles.
This can frequently be a good move, especially in places you feel obligated to be high on the spectrum of formality, jargon, technical language, etc.
Another thing to try: Synonymia is deliberate use of many synonyms. If you want to work your prose up to a place of elevation or scholarly tone, you could start from the core and go to borrowings or vice versa. Moving from elevation/scholarly to core is essentially the above style example.
You might do this across a passage (e.g., starting your essay with more French/Latin/Greek derived words and then ending with more core by the end to drive a point home; you might use core to grab attention at beginning of essay before ending with more “scholarly” language toward the end).
You could also do this in a sentence with a list. For instance:
So ambulate, take a stroll, stride on down, just walk out here.