I think I understand what you trying to do, but I don't think that's how GROUP inheritence work in Junos. Here is a short explanation of what I understand group to be.
I assume from your configuration that you made a GROUP called "global-policy" with those parameters.
Groups aren't used in the actual configuration. They are like defining a variable (like $policy = blah blah blah in other scripting languages).
So with your configuration, to actually use it you'll have to actually do
set security policies from-zone MGMT to-zone X apply-groups global-policy
where X is any zone. Now, this doesn't mean it'll apply to EVERY zone. You said you have 30 zones, so said if they are zone1 through zone30 you have to do
set security policies from-zone MGMT to-zone zone1 apply-groups global-policy
set security policies from-zone MGMT to-zone zone2 apply-groups global-policy
set security policies from-zone MGMT to-zone zone3 apply-groups global-policy
etc. for all 30 zones. This is how group works from my undetrstanding. and to check if it actually worked you'll use
show security policies | display inheritance
This should show you if each policy inherited the right configuration.
What you want to do though I am not sure of an easy way, maybe you could try using group AND wildcard range operation such as:
wildcard range set security policies from-zone MGMT to-zone zone[1-30] apply-groups global-policy
This, in theory would apply that policy to all 30 zones...
OR what you can do is just put EVERY SINGLE interface in the MGMT zone, and DENY ALL host-inbound traffic and allow only on certain interfaces....
maybe some one else have a better solution...