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I'm loving the archetype and will probably be playing a Psychic Detective soon. Consider that you can grab Color Spray right at first level to boost your combat capabilities and then trade it away at level 5 for a utility spell.
I personally recommend going with an Elf for this build. If you choose to use Strength for damage, you've got Longsword proficiency. For a Dex to Damage build you can use a Rapier from your class proficiencies, so drop Elven Weapon Familiarity to pick up Fey Thoughts and regain those class skills you lost.
So my plan would be Elf with Str: 10, Dex: 17, Con: 12, Int: 18, Wis: 12, Cha: 7. I'd swap EWP for Fey Thoughts, picking up Arcobatics and Climb as class skills. Weapon Finesse > Weapon Focus > Fencing Grace for my first three feats, retraining them around level 6 or 7 if I can get an Agile Rapier.
Note: At level 7 it would cost 1050 gp and 15 days to follow this plan, doable if the campaign allows that much down time. I also get to trade these out for either Expanded Phrenic Pool or Extra Investigator Talent feats, so that's money and time well spent in my book.
Damage output will be low at early levels, but Color Spray with an 18 Int should get me past the levels 1-3 hump that most Investigators have to deal with. At level 4 I'll have Studied Combat online, and Dex to damage at level 5. That's not too bad overall for melee options.
The fact that my spells don't have obvious verbal and somatic components makes me a very sneaky character. With Trap Finding and Mage Hand I'm awfully close to being an Arcane Trickster. I've also got 10 skill points per level and can boost my skill rolls with additional dice.
As a final thought, were I to Gestalt this I'd probably roll with my old Bladebound Kensai build. That would provide a huge boost to damage potential, give me two forms of spell casting keyed on Int and would let me go with a Str build instead of a Dex build (since you get Mage Armor from the Psychic spells at level 1).