We can farm every crop except melons and pumpkins on other players islands. I think this could be solved one of two ways 1. Harvest Axe - It would have all the upgrades that you normally would have on your Premium Harvest Hoe but it would be axe so you can destroy only pumpkins and melons. It would have auto-sell, treasure hunter, exp boost, and double crops like a normal hh and you would get points based on leveling up. Just like hh just for pumpkins and melons. 2. Phoe Upgrade - You could add a new upgrade to the already existing phoe but it upgrades your hh to be able to harvest melons and pumpkins and as you level it up the efficiency goes up. Since it's only for two crops it should cost about 2 points per upgrade and wouldn't add a whole new item.
The harvest axe idea sounds pretty cool. Instead of having it like a premium harvest hoe, it could just be like the beginner enchanted iron harvest hoe that you receive when you first join the game as a beginner. I do think having it this way would allow the owners to implement it faster in game. Also I seen that your post has been up for almost 5 days and only 2 votes, if you want more interaction and voting on your suggestions, you should probably send the suggestions in the community discord in the submit-suggestions tab.