Is there some way to reduce or avoid the multi-attack penalty when throwing weapons?
So far the only thing I found is the Dual Thrower feat which is completely useless because it requires you to already hold both weapons and I couldn't find any way to draw two weapons with a single action.
If it helps I'm looking into Alchemist using bombs. Quick Bomber would let me throw up to 3 bombs in a round but that's hardly useful with standard attack penalties.
This feat you've mentioned is only limited by needing to have two bombs in your hands, which can be worked around:
Valet Familiar: You can spend one action to have them place two bombs in your hands, and there's many ways to get a familiar like the 1st-level alchemist feat Alchemical Familiar
Double Brew: As a 9th-level alchemist you can use Quick Alchemy to spontaneously create two bombs as a single action, ready to be thrown.
Start combat with two bombs ready: Only works for the first turn, but in practice your resources might be limited where early on this is sufficient.
Pursuing this feat to make two strikes without MAP also opens up future options like the 14th-level feat Dual Onslaught. For most Dual-Weapon Warriors getting a free successful attack once a round is good, but many bombs have very powerful effects on a success beyond damage.