I believe I've set the time correctly, but the values I'm entering in setDS3231time don't look anything like the values I'm seeing in the Serial Monitor:
45:165:85 165/165/165 Day of week:
45:165:85 165/165/165 Day of week:
45:165:85 165/165/165 Day of week:
45:165:85 165/165/165 Day of week:
45:165:85 165/165/165 Day of week:
45:165:85 165/165/165 Day of week:
Perhaps you are using wrong SDA/SCL pins?
These are only A4 and A5 with Arduino UNO or other boards using Atmega328.
Different boards use different pins for SDA/SCL.
What you see is "zero reading" from the I2C bus, combined with a "no-error-handling-sketch" that loves to displays nonsense instead of useful error messages.
That is caused by reading all ones from the bus and is usually caused by a wiring error.
Make certain that you have SDA and SCL wired to the correct pins. Usually you also have to have 4.7k pullup resistors on both SDA and SCL (although some devices have them built in).