I heard there's a way to edit the game files to give you better prices selling things at shops.

Does anyone know where this setting is located? I've looked in:
C:\Program Files (x86)\GalaxyClient\Games\BATTLETECH\BattleTech_Data\StreamingAssets\data\shops

and couldn't find anything. I've looked at the files for ammunition and components, and see a "discountmodifier" which is set to 1.0 but not any kind of a resale modifier.

If anyone knows where the option is, I would love to know.

Try the SimGameConstants.json and search for :

"ShopSellModifier": 0.32,
"ShopSellDamagedModifier": 0.08,
"ShopWarnBeforeSellingPriceMinimum": 100000,
"MechScrapModifier": 0.08,
"MechLabRefundModifier": 0.9,
"RecoveredChassisShopModifier" : 0.9,

I put a detailed post here as a response but it appears to have been removed for some reason.

No, I see - the thread was double posted.