There will be a lot of people that disagree with this, but realistically outside of rare absolutely fantastic letters with great stories that portray you in a unique light, and terrible letters that warn admissions committees about you, letters aren't going to make or break your application.
Good letters of recommendation are a dime a dozen. Letter writers are people that have good rapport with the person they're writing letters for, so of course they're all going to talk highly about the applicant. Not to mention, it's not uncommon for letter writers to tell the applicant to write it themselves and they will sign it. Letters tell you far less about the applicant than their academic metrics, their extracurriculars and their personal statement.
Anecdotal, but I never attended office hours and asked professors that didn't know me personally, and my application cycle has been pretty successful. I really think my letter writers appreciated that I wasn't someone showing up with pointless questions every time they had office hours, even if it resulted in a less personal letter. It has to be annoying to have students kiss up to you all semester with the intentions of requesting a letter.
I wouldn't worry about it. Focus on the other aspects of your application. I suppose I can't speak for top schools where every aspect is make or break, but letters are generally second-tier in importance.
