A phrase is abbreviated, and it would be easy to figure out why "と" is required.
So, the sentence is comparing さっき「言ってたこと」 and 言ってること, so that it requires と.
That sentence is often used when someone is complaining/accusing that one changes his/her explanation.
My Japanese dictionary says that はるばる is an adverb and sometimes is used with と. So you are right — the existence of と doesn’t change the grammatical role of はるばる. In fact, はるばる and はるばると are pretty much the same in terms of both usage and meaning.
As background, sometimes adverbs in Japanese are followed by と or に. (See https://kotobank.jp/word/副詞-123983; ...
The short answer is that you can just stack them. For instance:
This machine will make doughnuts simply and quickly.
The longer answer is that you can have multiple adverbs in a sentence, but just like in English, where you put them changes what it applies to. Quantifier adverbs (とても, ちょっと, あまり etc.) are great to demonstrate ...