So, if socialism/communism is not completely inevitable, how do I form appropriate arguments for the use of Marxism to advance the cause of the proletariat against that of the ruling bourgeosie without falling to arguments about inevitability

This one's easy on the surface. Just don't say it's inevitable. Please let us know what you need to rely on inevitability at all.

Under the surface, this is hard if you don't have other arguments. So we need to help you develop other argument.

how do I form appropriate arguments for the use of Marxism to advance the cause of the proletariat against that of the ruling bourgeosie without falling to arguments about [...] “the greater good”

This is a great question, because it starts to move you away from the morality of good and evil, it moves you away from the position of the victim and the demand for justice. I think the greater good argument is still rhetorically useful, but it's not the crux of the Marxist argument and analysis. So, good on you from moving away from this, just don't throw it out in the trash and keep it around for when it's useful.

how do I form appropriate arguments for the use of Marxism to advance the cause of the proletariat against that of the ruling bourgeosie without falling to arguments about [...] the capitalists being “evil”

This is another good one, not just because it helps you move away from morality but because it forces you to enrich your understanding of exploitation. Exploitation sounds like a bad word to most people, but exploitation when used in ecology is not a bad word, it's a description of how components of the ecosystem relate to each other. For example, a particular insect exploits the abundance of sugars present in deciduous trees in order to provide it the energy it needs to reproduce. So, if exploitation is amoral, what's the argument here?

showing the ideologically backwards, or even intermediate, the way of proper Marxist analysis?

This was me at one point. It comes with the territory of growing up in liberal democracies. We're trained to argue this way, to reason this way, and to think this way. The process of coming to understand Marxism is difficult precisely because it requires us to unlearn so much of what we have previously learned and everyone around us constantly reinforces.

The "proper" Marxist analysis is one that sees society as the subject of analysis, not people, not morals, not ideas. Marx's work established him as the progenitor of Sociology, no cap. I didn't realize that at first, but prior to his work and Engel's work, there was no scientific field of sociology. They created it.

So if society is the subject of analysis, how did they come to the conclusions they came to? First, what conclusions did they come to? There's a few that highly relevant to your current question:

1. It is possible to analyze society as a system that follows laws through causal relationships.
2. When analyzing society in this way, the material conditions, that is, those aspects of reality that are causally linked, can explain how society got where it is, how it functions today, and how it evolve.
3. Society is a system, and as such, society must continually reproduce itself. That is to say, society is in a state of dynamic equilibrium.
4. Without equilibrium society, like all systems, will devolve (or collapse) to an earlier state, which can be as far as back as the state prior to the systems very existence. For example, capitalism could collapse back to feudalism, or human society could collapse to a state of the world without humans.
5. The society we find ourselves in has contradictory processes that undermine that equilibrium. Therefore, society is in a state of unstable dynamic equilibrium. An example of a contradictory process us the process by which the owners exploit the workers: the owners use their power to ensure worker's needs are not fully met, the workers work to meet their needs, the product of the workers is what gives the owners the power to ensure worker's needs are not fully met.
6. The consequence of these contradictions threaten to collapse society, thus society must do something about them. Resolve them, or intervene on itself to resolve the acute disequilibrium temporarily. An example of these interventions are physically oppressing workers who are demanding their needs met. These interventions are also contradictory - deploying physical violence to quell uprising creates the conditions that require more physical violence to quell the same uprising, etc.
7. Long story short - it is possible to create a society that exhibits a stable equilibrium without the contradictions we see today. By the analysis, this society must be classless, moneyless, and stateless. To make it easier to talk about, we call that arrangement of society "communism".

So, with all these points taken for granted for this conversation (read more Marx, Engels, Lenin, Mao, and secondary sources to deepen your understanding of the above and understand the arguments behind these points).... how can we argue without "inevitability, the greater good, the capitalists being evil, et cetera?"

You take the position of systems explainer and you let your audience inject their own morality. It is not a question of morality whether society collapses and humans go extinct. However, for those of you in the audience who rely on society existing, I would like to explain to you how society reproduces itself and its failure modes. Based on the analysis, society is in danger of collapsing due to contradictions. Here's how that works. Based on the analysis, we can stop society from collapsing, if we choose to. Here's what it would need. (eliminate current contradictions, move to stateless, moneyless, classless) Here's how that would work. Here's why your alternatives don't work. I'm not saying we have to choose communism, but if we choose to maintain human society, then communism is the only way for that to happen. Otherwise, the contradictions will destabilize and collapse society back to earlier forms, up to and including extinction.

It's mechanical, it's causal, it's amoral, it's explanatory. We don't need to exist. But if you want to exist, you need human society. If you need human society, then communism is the only form that can sustain itself. Class-based society will collapse and in fact has been in the process of managing it's unstable equilibrium since classes emerged. Here's the analysis, here's the evidence from history, here's the contemporary evidence.

Once you get here in your understanding and debate posture, you'll start getting into real arguments with anti-communists about their alternative solutions and you'll need to get better at understanding the analysis to proceed. You'll also start getting into real arguments with other leftists who disagree about how to bring it about. And you'll start to understand how Lenin both extended Marx's work as well as argued against and disproved some his assumptions (specifically that the most likely place for revolution was the industrialized European core and not the agrarian periphery).