Losslessly reducing framerate of a 'video of a video'

Question

I asked this yesterday but it was incorrectly closed as a dupe of question:Reduce video frame rate without dropping useful frames

The difference between that question and this question is - in that question the user has a video that was, via software, upscaled from a low framerate to a higher one, and they want to bring it back down. In my case, I have a full desktop recording that was natively captured and recorded at 60 FPS, however, within that desktop, there is a window which displays a video that I care about which is only playing at 30 fps. However, in the desktop recording there are motions at 60 FPS (e.g. my cursor).

--- Original question ---

I have a screenrecording of a video chat I had and the filesize is massive because the screen recording itself was done at 59.93 fps. However, I think the video chat was something like 15-30 fps. Plus it was a video chat, so the individual frames were obviously compressed as well.

I don't want to lose the quality of the video (it's already somewhat poor considering it was a vid chat). However, I'd like to reduce the filesize. I don't quite know how to best go about this though... I suppose my question boils down to:

1. Is there a way to somehow lower the framerate of the video in a way such that it is in sync with the framerate of the vid chat?
2. Are there any other compression options I have that I'm unaware of?

Here's the ffmpeg -i output if that helps:

Input #0, mov,mp4,m4a,3gp,3g2,mj2, from '.\Untitled1.mov':
  Metadata:
    major_brand     : qt
    minor_version   : 0
    compatible_brands: qt
    creation_time   : 2015-08-02T20:32:54.000000Z
    com.apple.quicktime.make: Apple
    com.apple.quicktime.model: MacBookAir4,2
    com.apple.quicktime.software: Mac OS X 10.10.4 (14E46)
    com.apple.quicktime.creationdate: 2015-08-02T12:46:10-0700
  Duration: 00:45:19.57, start: 0.000000, bitrate: 12981 kb/s
  Stream #0:0[0x1](und): Video: h264 (Main) (avc1 / 0x31637661), yuv420p(tv, bt709, progressive), 1438x874, 12974 kb/s, SAR 1:1 DAR 719:437, 59.93 fps, 60 tbr, 6k tbn (default)
    Metadata:
      creation_time   : 2015-08-02T20:32:54.000000Z
      handler_name    : Core Media Video
      vendor_id       : [0][0][0][0]
      encoder         : H.264

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