Hello!
So I can try ;-)
First, I presume, your configuration is like following:
- Hagen: Midi CH 1
- Mobius: Midi CH 2
- Timeline: Midi CH 3
- Big Sky: Midi CH 4
Now, you shall program your presets in Glab, so that every preset send Program Change (PC) to Hagen.
Here you can use different approaches:
1. You use the same Hagen sounds in different Glab banks e.g. you have 5 ground sounds such: clean (CH1, fx on, master 1), crunch (CH2, fx on, master 1), rhythm (CH3, fx off, master 1), wet rhythm (CH3, fx on, master 1), solo (CH4, fx on, master 2). Then you will program the PCs in the banks with the same numbers. This way when you change setting for your eg Clean sound, it will be changed in all banks without further programming. eg
Bank 1 (PCs

1 2 3 4 5 2 2 3 4 5
Bank 2 (PCs

2 2 3 3 5 1 1 3 4 5
...
2. You set the PCs in order from 1 to 120 (in 10 Glab banks). This way you must program every single preset in Hagen too:
Bank 1 (PCs

01 02 03 04 05 06 07 08 09 10
Bank 2 (PCs

11 12 13 14 15 16 17 18 19 20
...
When you set this, push the preset switch on Glab that you want to program, go to Hagen, push "Store", Hagen blinks, then push "Store" again, now the PC that you set in Glab for this preset will be stored by Hagen.
If it does not work as expected try:
- check if the MIDI Channel of Hagen is the same as you think (it is good explained how to set it in the Hagen manual)
- First push "Store" on Hagen, than push preset on Glab, than push "Store" on Hagen again
- try to connect the Hagen directly to Glab (not via Midi Thru from Strymon). If this works (better) than you shall use Midi Thru Box (one in, 4 outs) but be careful you need powered Thru Box here (eg from Glab). The pretty common "Midi Solutions" boxes does not work because Glab do not send power per Midi (here I am not 100% sure for GSC-4, until GSC-3 it was so).