IMO - A Bongo will cope a many Stingray tones and personality pretty well - even the HH and HS models. On top of that, the Bongo will have a ton of other options as well (just like the Stingray, it has a pretty wide range of tones!). I've owned Stingray Classics (a 5er), Sterling single-H, Sterling HH.
However, it won't be an exact replica. It'll be ... like an impersonation at best. It'll be in the ball park - heck, it'd be in the infield. But it won't be exact.
Again, that's IMO.
Out of all the Stingrays I have owned I have a preference for the two way EQ preamp and wonder if the loss of that would make me regret the change?

day, this 6-string is not for me. I'm more of a 4 & 5 string guy.