Trying to find matches to complex criteria

My brain hurts trying to figure this out, but I know there is a way.

I am trying to write a formula that does the following: For each Schedule-tab cell (that is, for each student and class period), search through the Survey-tab column that corresponds to the student's column to find the first class that is both ranked 6 and matches the class period and return both the ranking and the class name (from Survey-tab column B), if none is found, then search for the first class ranked 5, then for one ranked 4, then ranked 3, and if nothing is found, return "NO MATCH."

A complicating factor is that classes can be are either semester length or full year (both semesters), so a semester match could be from either. That is "B1" is the same as both "F1" and "S1" or a Full-Year First-Period Class is a match for both Fall Semester First Period and Spring Semester First Period.

(Ideally, I'd also like to double check the class's age range against the student's age and skip any classes the student is not eligible to take. The two digits after the student's initials are the student's age at the start of Fall semester. However, most students did not vote outside their age range, so I can clean that up manually.)

I apologize sincerely if this question has been asked before, but my brain is so twisted about trying to figure this out that I don't even know how to correctly phrase my search! If this has been addressed, I would very much appreciate being pointed toward the solution.

My Google Sheet (with identifying data replaced with random information): https://docs.google.com/spreadsheets/d/1RLkwrZPFss2ALv006aRvMwuGLQCN1l7OiSDCL70dYQ0/edit?usp=sharing

I tried INDEX and MATCH and REGEXMATCH and a few other things trying to make this happen, but I've never done anything so complicated before, and honestly, my attempts were too embarrassingly wrong to be worth sharing! But the real problem is that I deleted everything in a fit of frustration (before remembering that I could ask for help).

Added solution to your sheet here. Please do validate the results to make sure its pulling the results aptly.

=makearray(counta(A2:A13),counta(E1:AU1),lambda(r,c,ifna(let(a,sortn(filter(filter('Course Interest Survey'!A2:AS,('Course Interest Survey'!A1:AS1=index(E1:AU1,,c))+('Course Interest Survey'!A1:AS1="Classes")),('Course Interest Survey'!C2:C=index(A2:A13,r))+('Course Interest Survey'!C2:C=index(B2:B13,r))),1,,2,0),ifs(index(a,,2)>2,index(a,,2)&": "&index(a,,1),index(a,,2)<3,"NO MATCH")),"none scheduled")))

Another solution that works well enough except for marking "none scheduled" as "no match" (in this case, we only have one class period with nothing scheduled, so I can work around that). Sharing it here in case it's a better fit for someone facing the same problem.

This uses FILTER to find matches and then ARRAY_CONSTRAIN to limit the filtered results to the first match.

=ARRAY_CONSTRAIN(IFERROR(FILTER("6: " & 'Course Interest Survey'!$B$2:$B$50,('Course Interest Survey'!$C$2:$C$50='Course Schedule'!$A2)+('Course Interest Survey'!$C$2:$C$50='Course Schedule'!$B2),'Course Interest Survey'!D$2:D$50=6),IFERROR(FILTER("5: " & 'Course Interest Survey'!$B$2:$B$50,('Course Interest Survey'!$C$2:$C$50='Course Schedule'!$A2)+('Course Interest Survey'!$C$2:$C$50='Course Schedule'!$B2),'Course Interest Survey'!D$2:D$50=5),IFERROR(FILTER("4: " & 'Course Interest Survey'!$B$2:$B$50,('Course Interest Survey'!$C$2:$C$50='Course Schedule'!$A2)+('Course Interest Survey'!$C$2:$C$50='Course Schedule'!$B2),'Course Interest Survey'!D$2:D$50=4),IFERROR(FILTER("3: " & 'Course Interest Survey'!$B$2:$B$50,('Course Interest Survey'!$C$2:$C$50='Course Schedule'!$A2)+('Course Interest Survey'!$C$2:$C$50='Course Schedule'!$B2),'Course Interest Survey'!D$2:D$50=3),"NO MATCH")))),1,1)