"Let's not leave too much food."
Translation:음식을 너무 많이 남기지 맙시다.
너무 많이 too much is an (compound) adverb. As adverb, it can only modify adjective, verb or another adverb, i.e. in terms of word order, it can only precede either of those types of word (adjective or verb or another adverb).
음식 food is a noun. It would therefore be syntactically wrong to have "너무 많이 음식" (X) i.e. using adverb 너무 많이 to modify noun 음식.
To modify noun, one would need to use the adjective form of 너무 많이 i.e. 너무 많은.
Too much food = 너무 많은 음식
Don't leave too much food =
• 너무 많은 음식을 남기지 맙시다 OR
• 음식을 너무 많이 남기지 맙시다 [Lit. Don't leave too much of the food.]
In terms of common usage, the 2nd option is preferred.
Both 많을 and 많은 are attributive form of the predicative adjective 많다, and are used to modify noun.
많을 denotes the future connoting possibility/anticipation; while 많은, the present, represents fact.
많을 음식 = food that must be (or that is probably) plenty/probably plenty of food => expectation/speculation
많은 음식 = food that is plenty/plenty of food => fact
Food for thought.
Grammatically, an adverb as a componential adverb modifies a verb, an adjective or another adverb; as a sentential adverb, a sentence. An adverb cannot modify a noun.
너무 많이, too much is an adverb; 음식, food is a noun.
Your suggestion "너무 많이 음식을 남기지 맙시다" seems to indicate that 너무 많이 is used as a sentential adverb. Although grammatically acceptable, I would interpret your sentence to mean either,
Let's not leave food too often or,
Let's not make a habit of leaving food
To use 너무 많이 in the front position and still preserve the meaning of the English sentence, in my view 음식 would need to be converted to an adjective, 음식의 of the food
너무 많이 음식의 남기지 맙시다 Let's not leave too much of the food
I might be wrong in thinking so. But if wrong, I would welcome all constructive feedback.
• -(으)ㅂ시다 - propositive mode. = Let's / Shall we
This pattern is used to make suggestion or an order to a group of at least two speakers in which the speaker is included.
e.g. 점심 식사합시다 - Let's have lunch
• (으)십시오 - Imperative mode, polite but officious style = Do ...
This ,pattern implies an instruction, command or recommendation.
e.g. 거기 서 계시지 마시고 앉으십시오 - Don't stand there, do take a seat.