About the best I can think of would be to nest your two original sequences into a new one--this makes the nested sequences act like single clips in the nesting sequence. Assuming both sequences are the same, just different "eyes," you would sync those up in the nesting sequence and add edits to both nested clips. You could either edit there, or copy and paste those segments into a new sequence.
Orrrrr... here's a super sneaky way, that might work though I haven't tested it...
As above, put both of your original sequences (A1 and A2) into a new sequence (B), or you could copy and paste the original sequence edits (A1 and A2) into two tracks in a new sequence (B), e.g. Left Eye -> Video 1, Right Eye -> Video 2. When you've done that, drag this sequence (B) in the Project Panel to the New Item button at the bottom of the Project Panel; this will create another sequence (C) and nest sequence (B) in it. In sequence (C), right-click the nested sequence (B) and select Multi-camera > Enable. Edit your sequence, simply chunking out and rearranging as needed. Right now, this sequence just reflects what is on Multicam Angle #1, or the Left Eye.
Duplicate this sequence, so you have (C1) and (C2). Designate sequence (C1) as the Left Eye, and sequence (C2) as the Right Eye. Open up sequence (C2), select all the clips in it, right-click and go to Multi-camera > Camera 2; this will change all the edits from the left eye to the right eye. You can then export both independently (which is I assume what you have to do).
Techincally, you could do this easily in sequence (C); after making your edits and exporting the Left Eye, just select all, right-click, and go to Multi-camera > Camera 2 and export again. That would make it easier to re-edit, if you needed, since you'd only be dealing with one sequence.
If any of that doesn't make sense, let me know! This is not tested for this kind of application, but it should work!
Also, there might be some useful tips in the links (think I have updated them to the latest) in this ARTICLE. Some is on image acquisition, and you have already done that, so with some, it will not be until you get into the tutorial, will the editing tips be useful - maybe?