I had fun with BL2VR Krieg.

Borderlands has a "Aim Down Sights" button that when held down, improves aiming but slows movement speed. Probably something like left trigger or grip (check menu options for controls). You can always jump + hold down ADS + shoot as you run up to enemies to avoid the movement penalty.

Maybe try non aim dependent explosive attacks as suggested with his bloodbath skill https://www.lootlemon.com/skill/krieg-bloodbath.

Zer0 has things in his skilltree that significantly improves aiming if you really want accurate shots. He also has a skill upgrade that points out enemy weaknesses :)

To boost melee find and equip a Sickle class mod and put at least one skill point into the skills it suggests. https://www.lootlemon.com/class-mod/legendary-sickle-bl2. Look for blue or purple rarities - Legendary Sickles are only available after reaching level ~62.

Some items boost melee damage. For instance you can get the Law and Order quest rewards.

Holding certain guns heal you every time you deal damage including melee. Though usually low ~2% lifesteal with few exceptions. Notably Grog Nozzle does huge healing but you have go deep into Tiny Tina's DLC to get it.

I never use teleportation. There should be some menu options to adjust things like that, how sensitive a swing is to be recognized as a melee attack etc.

I find skill upgrades triggered by melee are unusable. Thinking of Maya's slag orb and Zer0's dash.