It seems very difficult to truly escape mold. What can a renter, who doesn’t have the resources to move or remediate, do to improve their environment with a modest budget?

Beyond remediation, invest in a HEPA vacuum to clean, and non-toxic cleaners to wipe down every square foot of the environment frequently, preferably daily. Have a portable HEPA air filtration unit, at minimum and ensure proper ventilation and air exchange with outside air that is filtered well.