I even used the artifact drop rate mod and increased the chances dramatically. Nothing. Just roots and yams - if that.
This is probably more on the exploit-y side but you did ask for exploits. (Also I don't know how the artifact drop rate mod affects any of this.)
If you dig up an artifact spot and then reset the day, the contents of that spot don't change, but if you sleep to the next day they will change. So what you can do is this:
- First thing in the morning, ride around the entire map and check every artifact spot. Make a note of any spots that contain anything you want.
- Reset the day. Now you can spend the day doing anything you want - just don't dig up any artifact spots unless you've determined that they contain what you want.
- Sleep to the next day. Most of the artifact spots will still be there, but they will contain different stuff than the day before. (Well, you could randomly get yam or whatever in an artifact spot two days in a row, but the point is it gets rerolled.)
- Rinse and repeat.
This unfortunately doesn't increase your chances of getting artifacts in any particular instance, but it will greatly increase the number of chances you get, since you can use one artifact spot multiple times this way. Plus this way you're not spending any in-game time.
The faster but arguably more exploity way to do the same thing is to download
this predictor app, which will tell you (among other things) what's in your artifact spots.
Note that I'm calling it an app and not a mod (even though it's on NexusMods) because it doesn't actually affect your game in any way, it doesn't change the save file or the code or anything. It's not a mod for the same reason the Stardew Predictor and Stardew Checkup websites aren't mods. Is it cheating? YMMV.
Credit to @Bla_De for creating the predictor app.