For something like that, I'd see about removing & replacing the cart assembly (cart/styli) and replace with another of same type (fit/mount).
And for a player like that, a low cost/budget cart assembly.
Besides online shopping, I look into forums (Audiokarma) sometimes for answers. Some of them folks are deep into these kind of things.
If for some reason the player doesn't work, there are several low cost Retro players on the market, don't know about the 78 though.
wow... I paid $500+ for my last cart (decent turntable/good LPs) and just under $150 for my old vintage table (for scratchy LPs). When I was online shopping, there were loads of carts under $50, also many way more than the $500+ I paid for my better table. But something like what you have, most budget minded for that kind of player & for grandma. Most would just like to hear something & see it play. My ears are still good, and I grew appreciating my audio gear. My wife doesn't care and wouldn't touch my audio gear so she has a Retro look thing that plays records and has AM/FM radio (was given to her) and since her ears are not as good as mine, its easy for her to use and she is happy with it.