I recently set a new record on Sheppard Software US Geography Level 3. I submitted the run but unfortunately I realized the moderator of the game, pianosandawesome, has been inactive for 4 months. How do I get my run verified?

You should make an attempt to contact them about it on their twitter first.

Generally speaking, if a moderator is inactive then you should follow @Tron_Javolta 's advice and attempt to contact them through one of the social media links on their profile. If they don't have social media links or are unresponsive after a reasonable amount of time, you can use this thread to request the site mods to make you a moderator: https://www.speedrun.com/The_Site/thread/63nr7

Just make sure you read the original post of that thread before posting in it.

Another thing to do would be to make a forum post, but other contacts are also hugely recommended.