inomfood
First of all, cp doesn't strip any EXIF data, the EXIF timestamps are stored in the file itself. I assume you mean the file system timestamps.
I don't use MTP but one idea I thought of is: create a zip/tar archive of the pictures you want to transfer, transfer using cp and then unzip on your phone.
I'm pretty sure this will preserve the filesystem timestamps.
Alternatively, you can correct the filesystem timestamps after the transfer by setting them to the EXIF timestamps using ExifTool.