The only other option I can think of is if you have a second drive installed in your desktop move the EFI(ESP) there but it could create boot problems so make a system image before hand in case it explodes in your face and brick your pc. Read this at Superuser.
If you do a reinstall don't forget to sync windows with onedrive and download your model drivers to your ext. HDD so you have them ready(burn to a DVD or place on a thumb drive for future use). then the only that will take a bit of time is installing programs(which the installers can also be downloaded and save ahead of time) also let windows backup your libraries using file history so you can restore them quickly after. Then custom install increasing your EFI partition to 260MB. should only take about an afternoon to reinstall everything. That's still much faster than Windows 7 and earlier.
Maybe KYHI can help you with this. He's really with command line partitioning. Write him to come to this thread to help.
You can also use diskpart to assign a drive letter to that 100MB volume so you can browse its contents
type> select disk 0
type> list volume
you will see a lot of volumes without drive letters assigned..
Now find the 100MB volume #
type> select volume # (# being the volume number without a drive letter)
type> assign letter=s
now you can browse the partition contents
you would first have to shrink "Resize" C by 50MB (Did 10GB for my test)
then "Move" the C partition over to fill the free space
move the 128MB partition over into the now create free space
then expand the system partition to fill free space
and click apply
But I do still wonder why your EFI partition is so full... You can clearly see the Free space in my EFI (SYSTEM) partition in the pic above