Decreae frame rate for better image quality

Hi Guys!
I am currently encoding videos for my website.

I a nutshell, here is my precise workflow.
I have my Pro Res files, at 23.976 fps, resolution 1080p progressive. (shot with a 7D)

These videos are mainly screenshots and talking heads.

I need to encode them in h264, mp4 container, 360p, 23.976fps
I am using CABAC, with a target at 400kbs with a max data rate of 200% and auto key framing on scene changes. Nothing unusual and I ve been pretty happy with the results so far.

The only problem I have is when the videos are played full screen. Resolution is too low. So I ve been trying to encode at 600p which is enough for what I need. But the bit rate required to achieve the same quality is a bit too high.

I have come to the conclusion that my only option was to drop frames in order to preserve a good quality to the frames left.

I am struggling with that one. I thought that choosing the 2:1 options would just drop one frame out of two and therefore preserve a certain flow and prevents jittering... but it is fairly noticeable. Especially on talking head.

Can some of you guys chime and share its knowledge when it comes to optimize image quality by dropping frames? How low can I go (coming from 23.976p) Is there a secret option or workflow that would smooth out the glitches and make it less noticeable?

thanks a bunch!!!!