As mentioned above, there are few options within the established limitations.
It was mentioned that raising strength with a tome or the Giant belt could help. The Gauntlet of ogre power are more common though (if your strength is below 19)
The insignia of claw you mentioned.
There are also a few tattoos from Tasha’s Cauldron of Everything.
The Eldritch Claw Tattoo
Magical Strikes. While the tattoo is on your skin, your unarmed strikes are considered magical for the purpose of overcoming immunity and resistance to nonmagical attacks, and you gain a +1 bonus to attack and damage rolls with unarmed strikes.
Eldritch Maul. As a bonus action, you can empower the tattoo for 1 minute. For the duration, each of your melee attacks with a weapon or an unarmed strike can reach a target up to 15 feet away from you, as inky tendrils launch toward the target. In addition, your melee attacks deal an extra 1d6 force damage on a hit. Once used, this bonus action can't be used again until the next dawn.
Coiling Grasp Tattoo
Grasping Tendrils. While the tattoo is on your skin, you can, as an
action, cause the tattoo to extrude into inky tendrils, which reach
for a creature you can see within 15 feet of you. The creature must
succeed on a DC 14 Strength saving throw or take 3d6 force damage and
be grappled by you. As an action, the creature can escape the grapple
by succeeding on a DC 14 Strength (Athletics) or Dexterity
(Acrobatics) check. The grapple also ends if you halt it (no action
required), if the creature is ever more than 15 feet away from you, or
if you use this tattoo on a different creature.
This one can allows for massive reach, which can also be optimized with opportunity attack.
Spells like Primal Savagery, Alter Self, or even polymorph can work pretty great. Enlarge/Reduce can also help you hit harder. Bless can help to hit, but not with damage.
To access spells yourself, Spellwrougth Tattoos, Spell Gems (the cool thing with this one is that you don’t have to concentrate, spell go for their full duration. The spell is actually cast and it’s the effect that is stored in the ring (unlike the other mentioned here where you have to cast yourself), so no verbal, somatic or components either (as those were already used when putting the spell into the gem) it can be more practical with a front-liner that isn’t a caster), and Ring of Spell Storing can be good option (though the first is a consumable)
There are also potions if this is not needed too often or you have a potion crafter in you group. Potion of Giant Strength, Potion of Growth, Potion of Heroism, or Potion of Giant Size.
Even more niche, and less likely to be offered by you DM are Dark Gifts from Von Richten’s Guide to Ravenloft.
The Dark Guift Second Skin Offers this
Transformation. You can cast the Alter Self spell to appear in your second form. When you do so, you gain the effects of that spell's Change Appearance option and cannot end it to gain the benefits of a different option. Casting alter self in this way requires no spell slot, and you must finish a long rest before you can cast it this way again. Your spellcasting ability for this spell is Intelligence, Wisdom, or Charisma (your choice when you gain this Dark Gift). If you have spell slots of 2nd level or higher, you can cast this spell with them.
When you cast Alter Self using this feature, some cosmetic aspect of
your second form remains after the spell ends. This visibly marks you
unless you actively hide or disguise it. The mark is a perceptible
change such as scaly skin, stunted wings, eyes without pupils, or
horns. The mark fades after you finish a long rest.
Whereas the Dark Gift Deathly Touch offer these Features.
Death Touch. You can focus your deadly touch against your foes. As an action, make one unarmed strike. On a hit, the target takes an additional 1d10 necrotic damage. This damage increases by 1d10 when you reach 5th level (2d10), 11th level (3d10), and 17th level (4d10).
Inescapable Death. When you hit a target with an attack roll and deal
necrotic damage, you ignore the target's resistance to that damage.
Withering Contact. When you start your turn grappling a creature or
grappled by it, the creature takes 1d10 necrotic damage.
Outside of that, there are some infusions and armours but they would probably clash with your build.
Classes, Races, and feats are generally the best way.
There are plenty of homebrew options and reskinning or tweaking of existing things. For example, Taldorei Campaign Guide Reborn has a Vestige of Divergence that are fistwrapt (Wraps of Dyamak), they require attunement by a monk, but if you change only that, you could gain between +1 ans +3 to unarmed strikes.
Lacanthropy could also be a thing.
That’s all that comes to mind at the moment.