Amanda H. answered 10/07/19
English and Beyond! Experienced Instructor: ESL, Writing, Literature
Hi Esther,
I think it's true that this will stand out to your reader. However, the language used is not as effective as it could be. Saying "I earnestly look forward" does not mean that same as I am excited or I am eager. Earnest means serious, with intense conviction. It's a bit odd, I'd even say incorrect, to use the adverb to modify look. Since the adverb modifies the verb, the meaning becomes 'I look serious' or I am intensely looking. While we'd like to expression enthusiasm, I don't think "earnestly look" is an effective modifier.
Alternatively, you could end this letter with one of these options, employing a more active verb or more appropriate adjectives and/or adverbs:
I eagerly await your response.
I'd be thrilled to hear from you.
I'm excited for an opportunity to discuss this further with you.
I sincerely hope. . .
I am genuinely excited/eager/invested/hopeful/interested
I agree that the phrase "I look forward to hearing from you" is used very frequently. You do not have to use it at all! Express your interest and enthusiasm in fresh way that represents your true feelings rather than triteness that mirrors what's been done before.