Your lesson is very ~ます focused. Keep in mind, always being formal is like keeping everyone around you at arm's-length, which might even wind up being rude in certain situations. So, you cannot neglect the plain form: 言う
田中さんは「猫が好きだ」と言った。
If you are quoting reported speech, you may use the ~ます form even if your speech is otherwise plain.
田中さんは「猫が好きです」と言った。
And, although you qualify "paired" with the word "often," you're not giving と justice with the amount of words it can be used with. Just a few for example:
と聞いた/と聞きました (heard)
と思った/と思いました (thought)
と怒鳴った/と怒鳴りました (shouted)
と叱った/と叱りました (scolded)
と probably works with all the Japanese equivalents for said bookisms.
As for the endings, keep in mind everything after 言 is just the conjugation of the verb, and all these examples happen to be past tense: "said." But, it can be "will say" (言う), it might be "can say" (言える), or "won't say" (言わない), or "even if said" (言っても), or--in the case of 言って--"please say." Although, to be honest, I think I'm missing something with the て form as I often see it ending sentences where it makes no sense as an imperative and is not connecting to anything else (the て form basically adds "and" to the end of the verb, and if nothing follows, it's assumed to attach to ください, making an informal but still somewhat polite imperative).
That said, in casual speech the whole thing can actually be replaced with just って:
田中さんは「猫が好きです」って。
