I've been playing around with Doomguy's stats and loadout, and I think I've hit a sweetspot. I'll list my changes and try to explain why I made them below:

Increased "Curse" stat from 0 to 3 - Back in his own world he deals with demons and all manner of hellish creatures on a daily basis. The Jammed are the closest to demons we have here in the Gungeon. Plus, it is an easy way to balance him starting with such strong stats and items.

Swapped out his Regular Shotgun for the Huntsman - In many doom games he carries this cursed demon sword. The Huntsman is a shotgun with an axe blade taped to it, which can destroy hostile bullets while you reload. The Huntsman also gives you 1 curse while it is in your inventory. It is the closest match I could find.

Reduced "MovementSpeed" stat from 10 to 7.5 - Combined with his Bionic Leg his movements speed was 11.5 before my change. Having such high movement speed is not only very disorienting for me, it is also just not very balanced. I fiddled around a bit and I think my change is perfect - not too fast, but also not too slow (seeing as you obviously intended for him to be a very fast character).

Changed "PlayerBulletScale" stat from 1 to 0.5 - The Doom Guy is from a world that is based on our Real World on many aspects, one of which is the size of the bullets compared to your gun's barrel. While reducing this stat to 0.5 still isn't completely "realistic", it does help a bit. This change in particular does not change a whole lot from a gameplay perspective, but is mostly to give this character a little something extra to make him more unique.

Changed "Health" stat from 3 to 2 AND added Old Crest to his loadout - I am still torn about this change though. Because of his Bionic Leg granting him 1 armour piece, I thought that removing 1 full heart and instead giving him another piece of armour would make his loadout more "balanced". This would mean he now has 2 full hearts and 2 armour pieces. Armour is also more effective against the Jammed - where a Jammed bullet would remove 2 half-hearts, it only removes 1 armour piece. And seeing as he'll be encountering more Jammed due to his high starting curse, giving him another piece of armour is just perfect. Plus, in the Abbey of the True Gun (access is granted by the Old Crest), in a few room layouts certain enemies are guaranteed to be Jammed. This only means more hellspawn to kill. So Old Crest it is!