There are different styles of picking. Some people use a pick in the manner of a galax player, where the pick (like the quill) sticks way out past the fingers and is strummed incessantly and vigorously. I do not play in that style, so I can't explain how to protect your instrument in that case.
I strum in the manner of a guitarist (no surprise after 40 years of playing the guitar). That means a couple of things. First, a homemade pick would never work for me because I want every pick to be exactly the same, the same shape, the same thickness, the same grippiness, etc. I like the idea of homemade picks but I just can't believe each milk bottle or margarine top is the same as every other one, and the inconsistencies would drive me nuts.
My other advice is very similar to that offered by Ken H. First, don't hold your pick tight. The pick should be loose in your hand and your fingers should be relaxed. Second, only the very tip of the pick should stick out past your finger. The bulk of the pick should sit squarely between your thumb and finger. Third, angle the pick so that the tip is toward you when strumming out and away from you when strumming in. And finally, the pick does not have to get down in between the strings. Think of the pick as gently gliding over the top of the strings rather than actually plucking them from below.
Hopefully those tips will help. At the very beginning of my video on flatpicking guitar techniques for modern dulcimer I go over how I hold, strum, and pick with a pick. Maybe it will help you. Maybe not.
And when you get your dream dulcimer, you might consider an ebony overlay on the fretboard. Ebony is so hard that your pick won't likely dent it.
Good luck. And have fun!