あなたが会社を辞めた理由は私 なりに 理解しています。
Would this translate to something like “speaking for myself”? As in, “I don’t know about the rest but… I get it”
That’s the self-effacing use of (first-person prounon) なりに, so, yes, it’s essentially “I understand it about as well as I can (from my perspective).” (Lit. “I understand it in my own way,” but that’s the effect, since it means the understanding is personal and obviously incomplete.)
If you wanted to emphasize the fact that you personally understood, in a way where you’re relatively confident your understanding is spot on, you’d use phrases like 個人的に instead. (Or just no adverb.) “Me, personally, I get it.”
The self-effacing quality isn’t built into なりの・に, just to be clear. It’s not an element that’s in play when appended to objects, adjectives, etc, but a byproduct of context when attached the speaker. “I did it my way … and it might be kind of sloppy or incomplete, but look, I’m trying.”
(Conversely, it can also be used as praise in a kind of round-about way if attached to a third party. 彼・彼女は自分なりに頑張りました. “They tried really hard for them/given their abilities.” (Literally, in a way that’s reasonable for them.) In that case another “for” phrase a la にしては would seem kind of harsh, since it would emphasize the low expectations instead of the effort. But that’s a pretty niche case and something you’d probably only hear in a context like a teacher discussing a student–and you’d never, ever say it to someone’s face. In comparison, 自分・私なりに, from the speaker, is fairly common in the self-effacing capacity shown above.)