Source to mod:
https://www.curseforge.com/minecraft/mc-mods/modern-beta

open-source too, i believe. the dev for this mod has been on a long hiatus. i played with your mod and modern's a bit.
there were some issues found. a broad amount features work such as mine intersection and river of lavas BUT -- i do not see any large expansive caves or lava falls.

this was tested using the modern_beta:modern_beta world-type followed by using "biomeProvider": "voronoi" setting.

Noted. I'm working on a series of compat patches. I'll add modern beta to the list of mods I'm verifying compatibility for.

It looks like Modern Beta fundamentally alters aspects of the worldgen process, which is causing one of the mixins to crash. I think I've got a fix but it looks like it's a lot of work at this time. I'll put it on the docket for 1.3.4/1.4. If my fix works, it'll be patched in 1.3.4 or 1.4.

Quick clarification: this is testing against the current CO codebase which includes a new way to check if worldgen is occurring in the overworld. During this test, I noticed some crashes, which is why I'm blabbering on about crashes :)

Regarding your feature request, 1.3.2+ includes an option to enable default worldgen alongside CO; you'll need to use that. Lavafalls are a rare occurrence due to how CO works, but I plan to change how lavafalls work in the future to make them more common.

Quick update, modern beta support needs to be shelved. MB appears to completely re-write major parts of Minecraft's worldgen, so my noise overrides don't have a chance to run. I'd have to formally set up CO as an MB mod in a sense, which is doable but a big timesink.

I'm closing this ticket. I'm sorry for this situation since I'd like to play on a world that has MB + CO one day.