Creating a "custom" Caladbolg

I've pretty much spent an hour each day trying to get the Sun Sigil for Tidus, doing the Catcher Chocobo minigame and the closest I've been overall is 7.5 seconds. I'm kinda fed up with it, and if I can't get the platinum because of this, so be it.

I was checking out the Caladbolg's abilities (Break Damage Limit, Triple Overdrive, Evade & Counter, Magic Counter). Those four abilities are possible to customize on a 4-slot sword for Tidus (60 Dark Matter, 30 Winning Formula, 1 Teleport Sphere, 16 Shining Gem), and I feel like I'd be able to get all of the materials much easily compared to how much time I've wasted trying to get a time of under 0 seconds with the minigame.

My (probably dumb) question is, would the game allow me to customize a weapon like that exactly? Would it also be renamed the Caladbolg automatically?