For character building purposes, the answer is very simple - get your spellsong check as high as possible. Everything else is irrelevant. Be aware that I have a rough calculation as to expected values at each level, although I'm not going to tell you what it is or how to get there.
Max ranks (3+lvl), synergy w/ Perform (+2), Skill Focus (+3), Charisma (4 + lvl/3 or thereabouts) is the start. You might get an extra +2 for a masterwork tool. Not counting magic items, spells, and other classes since I'm trying to work under assumptions similar to what you've described for Arhosa. And unfortunately you can't continue a spellsong's effect into the singing of the next without extra actions, so you can't buff your own Charisma with Face that Launched a Thousand Ships.
That said, for this game we're out of Arhosa, and homebrew is in.
Power of Cybernetics is your friend. Not an amazing, wow, super-awesome friend, but it's there for you in a pinch.
- Take Mastery Multiplier System for a +4 insight bonus right off the bat, plus more at higher levels if you pick up more energy. You can increase that bonus by another 2 by taking Systemic Reboot System for +1 capacity and +1 energy.
- The Omnitool module gives you that +2 circumstance from a masterwork tool even if the DM says no tools normally. If you start taking 10 (gained at 6th level of spellsinger) or you do a visor attachment, you can also get an enhancement bonus equal to the energy you invest (not very efficient, but if you're digging for every little bonus, it's an option).
Dip a level in the aura class of your choice for Motivate Charisma. Yo dawg, we heard you like Charisma checks, so we added your Charisma bonus to your Charisma bonus so you can Spellsong while you Spellsong.
- As meme-tioned, Motivate Charisma is a minor aura. It adds your aura bonus (equal to your Charisma modifier in the case of minor auras) as a morale bonus to Charisma and Charisma-based checks.
- A level of paladin gives you a couple of 0-level spells. Guidance, if nothing else, can get you a +1 competence bonus.
- I don't know most of the mantles, but I'm almost certain there's one that gives you a reroll 1/day. A level of divine mind will also give you a bit of psionics if you can scrounge up an interesting power.
- Marshal gives you a +1 major aura at 1st level. Motivate insight gives an insight bonus on one check per round. It won't stack with Mastery Multiplier System, but I'm mentioning it for completeness.
Codices of Spellshaping have a surprising amount of Charisma-friendly material (although it's got a surprising amount of material, period). Take a dip into a spellshaping class or two for some nice benefits.
- Flamespeaker gives you blaze 1/day, which is like a barbarian's rage, but with Cha and Dex bonuses and DR/magic instead of penalties, restrictions, and stats you don't care about. It also gives Cha to unarmored AC at 1st, and Cha to saves at 3rd.
- Impulse mage with the trance mage ACF gets a similar state, albeit with slightly lower bonuses, as the flamespeaker's blaze. On the upside, you get more formula and circles choices with that first level.
- The cambian race gives +2 Cha, a 1/day reroll, and a 1/day extra +2 Cha.
- Inspire Hope is a 1st-level minor formula from Brilliant Dawn. It's basically
heroism (+2 bonus on attack rolls, saves, and checks) as a swift action for 3 rounds, except that it's a sacred bonus. If you don't want to use class levels to learn it, a
robe of the Brilliant Dawn can give you access for 3000 gp.
- A couple of higher level Glimmering Moon formulae can help you. Luck of the Moon-Touched might not be too great, given that it requires a standard action for a chance at getting a later reroll, but if you ever get access to 5th-level formula (not likely in this game), Fortune of the Full Moon is a swift action for 5 rounds of +2 luck to virtually everything, and can be discharged for a single natural 20.
Can't say I'm too familiar with the rest of the homebrew scene, unfortunately.
Oh, and if you just want to get cheesy, custom magic items are in Core. Go go +30 bonus!