It's crazy that there is no option that simply says "No, NO ONE should be allowed to carry guns at school"

Furthermore, gun-free zones are often targets for shooters, as they know there will be no resistance.

Actually, despite that all sounding intuitive, studies show the opposite. For example, here's an excerpt from a study published in 2021 by the US Department of Justice (https://www.ojp.gov/ncjrs/virtual-library/abstracts/presence-armed-school-officials-and-fatal-and-nonfatal-gunshot):

"However, the data suggest no association between having an armed officer and deterrence of violence in these cases. An armed officer on the scene was the number one factor associated with increased casualties after the perpetrators’ use of assault rifles or submachine guns. The well-documented weapons effect explains that the presence of a weapon increases aggression. Whenever firearms are present, there is room for error, and even highly trained officers get split-second decisions wrong. Prior research suggests that many school shooters are actively suicidal, intending to die in the act, so an armed officer may be an incentive rather than a deterrent. The majority of shooters who target schools are students of the school, calling into question the effectiveness of hardened security and active shooter drills."

What do you think would be the best way to ensure the safety of students and staff while still respecting the Second Amendment?

Easy: national gun control, which has successfully and empirically worked in every single nation that institutes it, and is also the only solution that has ever proven objective results. National gun registration, background checks, mandatory training and licensing and insurance for each class of gun, etc...all of which are bare-minimum common sense gun laws that don't even require any kind of gun bans, and would even further protections for the responsible gun owners.

Additionally, if we want to actually solve not just the gun problem, but also tangibly address the rampant mental health crisis, then universal healthcare, including mental healthcare, is also an absolute necessity, as again seen in nearly every other industrialized nation. There are already a vast number of policies and programs that have long been objectively proven to solve these issues, yet for some reason (political and corporate profit at our expense) the media insists that this is some kind of complicated or unsolvable issue, when it is not either of those...