No idea who should write my LORs

[Olymerase]

I'm hoping to apply for an MS in Biostatistics at UF next year, so I need to start thinking about how to cultivate LOR-worthy relationships with my professors. The problem is, UF is huge. The classes are huge. You're lost in a sea of hundreds. Many of my professors outright have "Zero LOR" policies because they just can't handle being bombarded with 70, 80, 100+ requests for LORs every year.

The second problem is, it's Biostats. There aren't really any prelim biostats classes I can take right now - just bio, math, and stats classes - so I can't really get amazing letters from people actually IN that field. It would be cool if I was an econ major, had econ professors, and was applying for an econ MS. But that's not the case. My LORs would be from molecular bio professors, or the professor of a Calc 2 class with 400+ students.

I have a couple of professors from past years that would probably write me decent letters, but they just aren't in the biostats field at all. They are in the softer life sciences.

So yeah, not really sure how to overcome the problem of being in massive classes where professors make themselves unavailable to any type of impression that might garner a decent LOR. Are MS applicants generally expected to KNOW the professors personally, or is it more of a "This student had good grades, was proactive in communicating with me about course content, generally a solid A student."

....help