Actually all I can share is that quite often my camera can't focus on wide angle, but when it locks everything is just fine. It's not connected with anything like shutter speed, it's only AF system.Besides, I was told by one technician that this is impossible to repair, though I'm not sure now that he's competent.
I'm gonna AFMA it this week, hope it'll help.
I wish you'd be a little more clear with your problem description. So far I think you've described two very different problems, one with a 35 f1.4 lens, and another with a 16-35.
I might be reading a little too much between the lines here, but it sounds to me like you can't even lock focus with the 16-35? In one shot AF mode, I would expect that to only happen if you're shooting at a very low contrast target (white wall, clear blue sky, no light etc) or closer than the MFD.
If that's the case, I'd send them in, with a clear description of what you're doing and what's going wrong.