I recently saw Wickedy Chickedy (she’s a SDV streamer) search for a snake vertebrae on Ginger Island. According her, the artifact spots can give you different items, depending on how many times you dig before you hoe the artifact spot. Changing the order you dig up multiple spots can work too- or at least it worked for the snake fossils. It seems monotonous but some artifacts are cursed. It may be worth trying in town.
I *think* that's only for the snake vertebra where # of tiles hoed affects it -
@BlaDe can probably confirm.
However, if you check an artifact spot and don't get what you want, what you can do it reset the day, avoid checking it that day, and sleep to the next day and then check it again. It'll give something different. This way you can check the same artifact spot multiple times (although it will eventually disappear between days). Some people this is cheating and others don't, YMMV, but if you're at the point of wanting to install mods, this might be a simpler way.
Also, what you can do is go to Skull Caverns, and just repeatedly go in and out of floor 1, killing any ghosts you see (maybe break some rocks along the way, or just break rocks if you don't want to fight). Daggers are good for this since the special attack pins them in place, negating the big knockback ghosts have. If you feel like you're in danger of dying, don't get too far from the entrance, you can just exit and eat in safety. You should get a decent amount of omni geodes that you can trade for artifact troves, which have a 3.7% chance of giving both the chipped amphora and the ancient sword.
Or if you're on PC, you can just get one or two artifact troves, and then use the Stardew Predictor website to figure out how many geodes you need to open before opening a trove to get what you want.
