If a 2.5x slomo is not what you wanted, then you will either have to shoot a different rate such as 48fps for a 2x slomo, etc. or manipulate the speed with a motion effect in Media Composer.
Take a look at some of the settings such as progressive/interlace as it can change the overall look and frame rate adjustment you are doing. I did a quick blog on it here: https://24p.com/wordpress/?p=70
You will want to play with Field Motion settings to see what it looks like – also a lesson I learned in the process is when frame stepping/field stepping through a clip, make sure your timeline is set to green/green mode as you will be missing 1/2 the information when looking at it (not when rendering or transcoding).
Also, when you say you are opening the sources in a 60fps project, there is only one that does that; a 720p/59.94 project. 1080i/59.94 is a 29.97fps project that is interlace so a different motion adapter will be tagged on the source clip when opening it in a 23.976p project.
The green dot goes away if you’ve done a transcode in the current project as it will bake in whatever fame rate and such into the clip resulting in what is now considered a native 23.976 clip. Try opening the original clip from the “60fps” project again to see if the green dot reappears.
Michael