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It seems to be caused by Final Doomer's pistol start- the built-in GZ pistol start does not appear to cause this issue. My only guess is that FD's pistol start wipes your inventory 1 tic after the map loads, which screws with the startup sequence checks.

I'm not sure what you mean. I don't have anything like that, maybe it's some other mod you have enabled, or some strange incompatibility.

v1.4 is out. Sorry for the wait, I've been unable to work lately due to a mixture of burnout and personal issues.

Changelog:
-Added inventory display
-Remade the startup sequence and tweaked the death sequence
-Volume slider has been separated into categories
-Music can now be optionally muted on ...

It's not implemented yet, but next on the to-do list. Until then, you could use FlexiHUD's inventory display, as it is drawn independently of the main HUD and is compatible with other HUD mods.

v1.3 is out now, with a plethora of customizability, and powerup displays (at last)
Changelog:
-Added "compact mode" (experimental)
-Added some powerup displays
-Color of displays is fully customizable
-Ammo will no longer be drawn twice if ammotype 1 and 2 are the same
-Chance of displays ...

no, but I could see about adding it
Added, along with a small handful of other misc. things

v1.2 released, mainly focused on revamping the stat display and polishing the armor overlay animations.
Changelog:
-Updated armor damage animation
-Armor overlay colors are now entirely handled with code, should reduce file size a bit
-Added an idle animation to the armor overlay
-Updated number ...

Should be fixed now.

v1.1 is out now, with a nifty little showcase to go with it

Changelog:
-Added a 5th crack to the visor
-Fixed helmet top graphic using an outdated design without holes for the armor overlay (oops)
-Added a cool little animation when you are damaged and have armor

https://i.imgur.com/KNG2kF5.png

HUD mod I made, to practice ZScript and because most visor HUDs are bloated and/or outdated.
Has many features, including dynamic cracking, swaying, blood, startup/death sequences, and more.
Many features are also configurable, make sure to check the options ...

Can I modify this and implement it into my own mod?

I updated to the latest version (from 3.2.3) and I've noticed that several custom fonts (such as Input Mono and Terminal) don't work anymore, when they looked fine on older versions.

Doesn't seem to work for me.