Certain 59.94 clips play jittery on 23.98 timeline but play smoothly in the source window

None of this addresses the core issue at hand.

It's very common in documentary work.  If faster remastering is needed, you could look into a hardware solution by Taranex (now owned by Blackmagic Design) or Panasonic.  That, or split the rendering acrcoss multiple, fast workststions.

I didn't mention this earlier, but if you already have distribution in place make sure that the approach you're taking passes their quality control as soon as possible.  The last thing you want is for a program to get rejected due to how the archival shots were handled.  

None of these suggestions are reliastic for a 2-3 day turn around with close to 3.5 TB of footage being sent to me. You'd have to be crazy (and out of external hard drive space) to round trip those to AE or Topaz when you could just nest the 23.98 sequence into a 59.94 for output and put the problematic 59.94 shots on layer v2 within the nest.  I don't recommend sharing this idea with anyone else. Not practical.

@rachelcenter 

Any difference in temporal resolution (frame rate) is prone to not playing back well in a Timeline - even more so when dividing the Source Footage frame rate by the Timeline frame rate does not result in a whole number.

Try enabling Optical Flow for Time Interpolation in the Speed/Duration dialog box for each 59.94 clip in your 23.98 Timeline.  You’ll want to select the Clips afterward and then choose Sequence > Render Selection.  Then play the footage with Playback Resolution set to Full.  If that looks good, be sure that Optical Flow is also enabled whenever you export.

If After Effects is part of your subscription plan then another option is to roundtrip the 59.94 Clips to After Effects where you can use Timewarp to remaster the frame rate.

Topaz Labs Video AI is worth a try as well to remaster the frame rate if you are not liking the Optical Flow or Timewarp results.  Topaz Labs offers a trial version, but if you decide you like it the best, it is a separate purchase. 

Each of these options take some time to render. While revising rough cuts, I would use a Clip Label to easily identify the 59.94 clips and then take the time to remaster those based on what’s in your fine cut.

https://community.adobe.com/t5/premiere-pro-discussions/how-can-i-determine-if-this-frame-rate-issue-is-stemming-from-the-clips-i-m-given-or-premiere/m-p/13514350#M496289

As I understand it the source monitor plays back any clip at its native framerate and resolution, it's only when placed in a sequence that the framerate changes.