5-8% Strength for 4.5s on Kill. Stacks 5 times.
Up to 5-20% Strength based on the charge time of your heavy attacks. Stacks 3 times.
5-8% Strength every 0.4 seconds while aiming, stacking 5 times. Discharges all stacks upon firing.
5-8% Strength for every shot fired during continuous fire. Stacks 5 times.
My own take on the [Absolutely-Not-Meta-But-Still-Fun] grenadier Gauntlet Gunlugger.
Take whatever melee you want, the cleaver is just a good all-rounder.
With towering presence, lynchpin, and +60% toughness Regen, you should get your coherency toughness back very quickly and reliably.
Big boom won't likely help much with damage but you should more reliably hit 5 enemies with it and get your reload speed boost, which is sorely needed on the gauntlet.
Shattering impact is less good on the gauntlet than you'd think, blaze away is a much more reliable power boost, especially during point blank barrage.