I've never failed a speech check since I found Reginald's suit, level 6 charisma, plus 3 for Reg, +1 glasses, +1 hat = 11 charisma. (I also have 1 perk in the Ladykiller). perhaps that gives me 110% chance of succeeding on the dice roll, I'm not sure the inner workings.
I change before each speech challenge. Its probably uncomfortable for the person I'm talking to, but they seem to like it as they always acquiesce.
On the downer side, I realize I may have missed out on some missions with these speech checks, for instance, I didn't have to do crap for the Children of Atom..
But for the OP, if you don't want to up Charisma. you could get +4 by changing into common items, and +5 with graqe mentats for a total of 10, and though I always play with 11, I think that will suffice for any red challenge. I would also advise to just go ahead and get 6 Charisma so you can get local leader, but it sounds like you've played the game through a few times so maybe you don't want to deal with multiple settlements on this play through.