It has been a long time since I took a look at this build, and while it was certainly still functional post-Sisters of Parvos, it deserves to be freshened up.

After all this time, is it still possible to use [Kogake Prime] with minimal investment?

Yes. At the absolute, bare minimum, all you need is an Orokin Catalyst to make this weapon work. The Exilus slot is entirely superfluous (honestly just there to show you every slot can be filled without using a single Forma), and the only real thing that can push the build's strengths is a Melee Arcane.

Melee Duplicate, Crits, and Multihits

This build is focused on taking advantage of what would otherwise be huge demerits for the [Kogake Prime]; low Critrate and substandard Crit DMG. Ever since the enemy Damage Type Modifier rework in [Jade] Shadows, Impact damage has actually become a viable damage type, with some niche use cases to make it outright desirable.

And even before that time, it served a benefit on the [Kogake Prime] that it still serves now; it exists, and therefor triggers [Shattering Impact].

The premise of the build is simple enough; combine [Shattering Impact] with Corrosive Status, leveraging the [Kogake Prime]'s high Status Chance to decimate enemy armor with a flurry of blows. However, Whispers in the Walls added something that takes this build further; Melee Duplicate.

On Base Critical Hits (AKA: Yellow Crits/Tier 1 Crits), your attacks hit twice. Conveniently, we can take advantage of the [Kogake Prime]'s low crit chance and still have 100% slot efficiency by using [Galvanized Steel] and [Blood Rush]; at 12x Melee Combo, this gives us a Crit Chance of 104%, guaranteeing every attack lands twice.

These doubled hits roll their own Crits and Status separately, which means at max combo, every hit has a chance to apply 2 Stacks of Corrosive, and is guaranteed to strip 12 armor flat from [Shattering Impact]. And though it's only a small bonus, when fully stacked, [Galvanized Steel] boosts the Crit Damage multiplier to 3.96x, which while still bad comparatively to other melees, covers some of the [Kogake]'s weakness in the process of amping up its effectiveness.

Why not use Melee Exposure to open up other Elements?

Melee Exposure requires you to cast abilities at minimum 4 times and then semi-frequently thereafter to maintain its effect, and all it would really do is compete for Status proc chance with whatever other elements you put on the build - on top of forcing you to potentially account for lost Status Chance if you go for a single element like Electricity or Heat.

Simply put, for the goal of this build, Melee Duplicate trumps all other options. The double hit is incredibly strong for maximizing armor strip.