Solid GPA but a giant black hole in my transcript

[prEhistory]

Hello all! I'm an incoming senior at UCLA. I plan to apply to archaeology master's programs next fall. My issue is that despite my decent GPA (3.6), I have 4 F's on my transcript. Basically I failed two classes, and retook them, and failed them again; all with F's. I know this must look absolutely awful on a transcript. I do have a pretty valid explanation for my bad performance, and this class is not in my major. I am wondering if top schools are likely to overlook these 4 F's for my GPA and other credentials (lab and research experience, good letters, etc). Unfortunately for me, the three schools that my research interests align with best are all top 10-15 programs. I am also curious if any grad schools calculate GPA differently in cases like this. For example, will grad schools factor all 4 F's into my cumulative GPA since currently only two of those 4 F's are being counted? I really appreciate any help and/or anecdotes you can offer me. Thanks!