I think your first translation got it right for the most part, but you made it more specific than the Korean sentence.
For example, it's unclear whether the original is talking about the speaker or for people in general - probably the latter.
Also, you can't take "대충 때우는 식으로 끼니" as in your title and make sense of it separately (see the structure below).
"절대 대충 때우는 식으로 끼니를 해결 할 수 없어요!"
=> 절대 [[대충 때우는 식으로] [끼니를 해결할]] 수 없어요!
=> 절대로 (absolutely) 대충(halfheartedly, halfway) 때우는(make do, fill the need) 식으로(like, in such a way) 끼니(meal)를 해결햘(take care of) 수 없어요(can't do).
=> You just can't make do with a quick filler for your meal.
The second sentence is unclear about 확고한 철학.
It can be a philosophy of the speaker or of HMFood. I think the former is more likely.
"HMFood과 인연이 닿은 것도 미식에 대한 확고한 철학때문이였다."
=> It was also because of (my? / their?) firm philosophy about gourmet eating that I came to know HMFood.