I don't know what an egg farmer is either.

But I found a lot of this fun of the game opened up when I went into the unlocks and secrets menu and found out there's things I could do to open up different game modes, difficulties, etc

You can activate modifiers that makes more enemies spawn, faster etc. Later maps have different conditions. There is variety for what the game is.

And that is what I adore about the game. Every time it got boring another item,mechanic, secret showed up.

came close a few times

Since you can't see death's life, I'm going to be the first one to say you probably haven't come close :)

I think fighting death just takes too long for me to really feel like starting over when I fail

There are a few "very slow" builds, but if you don't take Death out in 20 seconds or less, odds are really good that your build can't even come close. Which is ok. Killing death is a very specific goal and most builds aren't designed for it.

The thirty minute grind the game is built around just felt rough to me

If you play a bit longer, you're able to reduce that to 15 minutes. Very few things are actually hard-gated to 30 minutes at all. Most unlocks are driven by character level; if you can hit level 80+ in less than 5 minutes, then you're good.

Eggs are what you get for killing Guardians and the Reaper, or purchased from the merchant. They provide a small permanent bonus to 1 of the active character's stats. Egg farmer is just a massive gold farmer that you can use to repeatedly purchase many eggs on both themselves and then other characters for the stat bumps. But it really is a different kind of build.

While, the Grim Reaper isn't really THE goal of most runs, just getting to him is enough to let you get several achievements, but getting that first kill is sweet, and you don't even need to cheese it anymore, it takes a few weapons plus other decent DPS.

The achievements really are the general on ramp to most of the game, rather than just getting to 30 mins, look at them, figure out a few to try for on the next run and then trying to solve that puzzle. Getting to 30mins with weapons you've used on characters you've used in a map you've already beaten without some other goal, can definitely be boring to do repeatedly. But surviving just 18min on Bat Country to unlock Chaos Malachite can be a real challenge if you aren't well leveled/lucky/skilled, preferably more than 1 of those.