Progenitor for Toxin

Organ Shatter

Many of us do NOT like banes; I get it. Fuck the bane lol. Throw Organ Shatter and I think you'll be happy about it. You lose the triple dip, but you get a little bit of Critical Damage instead. It's also advantageous to run Organ Shatter against enemies who do not have a bane yet: Scaldra and Techrot.
Melee Crescendo

Crescendo when paired with a frame that can cause finishers can be a nice touch to get this weapon well into the 10s of millions of damage. Airburst, Desiccation, Savage Silence, and Radial Blind are all methods via Warframe abilities, and Vazarin Focus school is another for stacking finishers. Coda Bassocyst is another amazing option, considering the theme of these weapons. We can then mod into pure toxin and add Weeping Wounds over Galvanized Reflex.

Melee Influence & Gas/Viral + Electricity

Melee Influence seems to be the popular choice for weapons that nobody seems to have an idea about. With that being said, it's still a viable option. We can make influence work by modding in for full Electric and going Electricity on the Progenitor. Bane mods have a double dipping effect on DoT weapons. This is true; however, Melee Influence has a triple dipping effect. 1.55x on the main damage multiplier. 1.55x on the DoT effect. 1.55x AGAIN on the spread through Melee Influence. The way to navigate through doing electric damage would be to mod in either Viral + Electricity or Gas + Electricity. We'll still get the toxin status chance on slams, moddable by the toxin mod (regardless of if it's combined or not).