1. The Cap: I can't add to what folks who've seen it have said. It's likely good and I think you should feel about confident as you can without a photo match, which can be difficult with caps.

2. The autograph: I am not an autograph expert, but I think the signature looks good base on other signatures I've seen. Remember, signing the underside of the brim of a baseball cap isn't like signing a nice, smooth paper item or photo. Particularly because of the raised stitching. And items like these are often signed while the player is standing and holding with one hand while signing with the other, sometimes while in a rush. All of this can lead to a signature that's not going to look like a signed photo.

3. Getting the cap signed again: It's your cap, and of course you should do what YOU want with it. If it were mine, I'd keep it as is. Given the assumption that this is Thomas's rookie cap and he has already signed it, probably around the time it was worn, I think it's perfect. You have a vintage signature on a vintage, worn cap, and the signature is on the place I prefer on a cap: underneath the brim. (I like game worn items to appear, for display purposes, exactly as they left the field, while placing any autographs in places that wouldn't have been seen by those watching the game, such as underneath the brim of a cap or down by the tags on a jersey. Different collectors have different preferences concerning this, and your preference is the one that counts for your item.) Overall, I think putting a modern signature on an item like this would detract from its vintage feel.