Conformation please, Explosive Missile + Directed Bomb

[Artemis Moonstar]

Directed Bomb:

Benefit: The alchemist can cause his bombs to splash in a 15-foot cone instead of a 5-foot-radius burst. The alchemist chooses the direction of the cone. If the attack misses, roll an additional 1d8 to determine the direction of the blast from where the bomb lands. This discovery can't be combined with the explosive bomb discovery.

Explosive Missile:

Benefit: As a standard action, the alchemist can infuse a single arrow, crossbow bolt, or one-handed firearm bullet with the power of his bomb, load the ammunition, and shoot the ranged weapon. He must be proficient with the weapon in order to accomplish this. When the infused ammunition hits its target, it deals damage normally and detonates as if the alchemist had thrown the bomb at the target. If the explosive missile misses, it does not detonate.

Just seeking clarification that this works together, since neither have an Asterisk next to them, on d20pfsrd or the Nethys archives, at least. I've got a gestalt game coming up, and I'm interested in running a Gulch Gunner, and feel like doing the whole alchemist dip thing (except as gestalt, so, full GS/Alch). Had the idea to utilize the Gulch Gunner's Powder Burns (and Belly Shot later) with Explosive Missile, using Directed Bomb to avoid blowing myself up, and get at the people behind the guy I'm shooting.

Regardless of the gestalt aspect, I'm now interested in trying this as an alchemist w/ gulch gunner multiclass in a basic game. If the two discoveries above work as I suspect they do.

In short: Alchemist uses (Insert bomb discovery here) while imbuing a crossbow bolt with his bomb. Fires it, and nails poor gobbo. Having utilized Directed Bomb, the bomb damage splashed back to blast the gobbo back up gobbo 1 had.