Any makeshift method would have damaged my older Trek carbon fork and titanium Chris King headset crown race. It doesn't extend enough beyond the fork crown to wedge in any kind of handheld wedge, screwdriver, chisel, etc., without damaging the crown and crown race.
I took it to the LBS and they used their Park tool. Took a minute, no damage, no drama. They charged $5. I gave them $10, and felt guilty later. Should have tipped more. They've done other freebie favors for me when they weren't busy.
I'm temporarily using an Orign8 headset, which is quite a bit wider in diameter and can probably be removed with makeshift crown race pulling tools. It extends quite a bit beyond the fork crown. And I don't really care if the Orign8 crown race is damaged, as long as the fork itself isn't damaged.
But I won't try to remove the King headset or similarly sized, tight fitting crown race, without a proper tool.
Regarding the pressed-in headset itself, I bought an inexpensive metal tool off Amazon with the springy split-end. Works exactly like the Park version. No problem with that tool. Ditto affordable presses. But the Park Tools crown race puller is head and shoulders above anything else on the market, with the exception of a couple of similarly designed and equally expensive tools.