This is my personal Funk & Soul machine:
Not a current guitar, but (in the S-Trem version) within your budget, and perfect for clean, funky sounds. And you will surely stand out with it, no matter how big the band grows
That just scared me.
Of course you can make anything work. Catfish Collins played a lot of Jazzmaster; Freddie Stone played a lot of Tele; Jimmy Nolen played a bunch of ES-175.
But when I think about funk, and certainly funk rhythm guitar, I first think of a 60s or 70s Strat, maybe even a hard tail, and a clean cutting amp -- a Twin Reverb or a Dual Showman or, heck, even a JC-120. Ernie Isley, Nile Rodgers, Curtis Mayfield, Eddie Hazel, all played a bunch of Strat. Nolen sometimes played a Japanese Strat copy.
Anything can work and it all depends. And I guess it matters how you and the guitar guitarists are going to divvy up the parts -- funky can involve some pretty dense rhythm guitar interlocking arrangements. Sometimes you might want to really blend tones, sometimes you might find you want contrast. I bet between the 335 and the Strat you'd have it all covered.
As a guy who plays a ton of soul and funk and sings - STRAT ALL DAY - ESP the 60s and 70s Reissues. They have balls without being too thin. Maybe HSS or put a SC sized HB in when you need it. A good amp with solid cleans and you are there. Get some good dirt boxes!
I sing and quite often I am in groups with NO guitar and I get to truly listen. I always enjoy the Strat guys the most. Esp when they have a good clean amp and dirt box OR a channel switcher with wicked cleans like a Mesa or Bogner.
Teles, 335's they are ALL good. But when it comes to tone the Strat always sits right in the mix, can do the notched sounds and its rarely ever harsh or too raunchy or thick on certain passages. As an example, I have a guy using an LP on a Jackson 5 tune and its too much sometimes.