Using 60 fps footage on 23.976 sequence without slowing down or dropping frames
You can not. You have contradicting parameters.

You need to make some decisions. Either:


Leave your project at 29.97 and drop 1 every 2 frames of your 60fps clip.
Leave your project at 29.97 and use all the frames of the 60 fps clip making it slow-motion 2x.
Change the project speed to 60fps and render twice every frame of the other footage.
Change the project speed to 60fps and make a timewarp filter on the 29.97 footage, what it does is inventing new pixels to the new frames, making it look smoother if the program used is a good one.
Preparing separated projects and making a strange arrangement of projectors projecting two framerates at some cinema screen... Nop, let us discard this idea and just keep the other 4 in mind.