What's the best way to reduce philtrum length when I have a lot of tooth show? (Photos)

I was interested in a lip lift when I got my rhinoplasty, but I already have a lot of teeth showing. My surgeon told me to just get lip fillers instead, but I didn't really like them. They made my lips fuller but didn't add much height, so the philtrum looked pretty much the same. I also tried a Botox lip flip, which I actually liked, but it still didn't make a big enough difference. Is there a better way to shorten my philtrum that won't show too much teeth?