For the easiest option, I'd just try to nudge him toward playing a scion or changeling descendant of something supernatural.

If that doesn't appeal, however, consider coming up with some exotic explanation of how a non-mortal acquired free will. There's been some threads on here before about playing a vampire-with-a-soul that might be relevant.

I once played a scion of a Rakshasa that had Modular Abilities without shape-shifting. My GM ruled that any power other than Wings that could reasonably be used by a mundane creature with the right anatomy was fair game (so, claws, spider climb, a custom Frog Leap power we wrote, etc.) as well as the "big 4" (speed, strength, toughness, recovery), but that anything involving psychic powers or spellcasting was off-limits. I combined this with a high Athletics, Fists, and Might score to be able to deal with just about any mundane physical obstacle easily, but I still couldn't do things the party spellcaster or more specialized physical builds could.

The fact that they can be destroyed during the day balances out the healing pretty well, I think. I mean, consider it according to the catch rules - +2 for the fact that it doesn't take a special weapon, just daytime (ANYONE can access the day, usually), and +1 for it being research-able.

As seen in the show, gargoyles have to go through a lot of trouble to make sure they aren't attacked during the day. Xanatos could have destroyed them any day he liked, and only didn't because he found them interesting and occasionally useful.

Time, knowledge, and connections are all important resources. You can't do a long ritual if the villain is going to blow up the city in two minutes from now. You can't solve the mystery with divination if you don't know the right questions or the right people to ask. And you can't kill an enemy or track their location with a ritual spell unless you've got his hair or blood or whatever to work with.

Actually it should be thrice per session. Exchanging one point of power or using an additional enchanted item slot grants an additional two uses.

Strangely enough, that's not quite right. I believe an extra slot gets you two extra uses, but reducing the power to increase uses only gets you a one-to-one trade in. I'm not quite sure why it was written that way, but it's there in the book for you to see.  Also, a crafting specialization of +1 frequency only increases uses by 1, not 2.

It's worth the effort to get a proper copy. It's a beautiful book, and unless you've got the money and access to a professional-quality printer, printing it yourself just won't look and feel as nice.

I think they both work pretty well as-is. I might consider making Dragonslayer only [-1], though, as it's a pretty darn specific power.

You should note that the Item of Power discount only applies once per character, no matter how many separate items he or she carries. Thus, a character using both the Shield and the Spear would have a total cost of [-5], as the items are currently written.

Finally, I'd suggest that the player of this character and the GM discuss exactly how that Catch will be handled. It sounds to me like ambushes would definitely bypass it, but what about a distracting maneuver invoked for effect to say he can't get the shield in position fast enough? What about AoE attacks or simultaneous attacks from multiple directions? I don't have specific answers for these; I just think it's an important conversation to have ahead of time so it doesn't become an argument during gameplay.

He could have temporarily drawn on his vampiric nature and hunger more deeply than usual to pull it off, which costs him in terms of self-control and being hungry later.

In other words, he spent a fate point to invoke an aspect related to his powers. 3 from Inhuman Strength + 2 from a Fate Point + 1 or more from a lucky roll could definitely add up to enough.