One thing you can do for the MIDI is to name the MIDI event/region by the instrument and preset name (regardless of whether it’s a factory or custom preset, both would have a name). I do this as a standard practice for the exact reason as what you are encountering, so that it’s always known what sound belongs to that MIDI region / track. The resultant audio tracks carry the same name.
Then just export the MIDI tracks and load them up in Cubase. The names will tell you what synth and preset to load.
In Logic, if your regions are cropped to edit out the silence, just join/glue each track’s content into one continuous region, and drag the left ends to make all the MIDI regions start at bar 1 so that you don’t have to figure out where to place them in Cubase. Then after they are exported, if you want the short clips to stay in Logic, then either undo the glue or just don’t re-save the project.
Alternatively if you absolutely don’t want full length regions, you can add the bar start # to the name of each region and manually place them. But to me, it’s easier to import them as one length starting at bar 1, then crop them out later.