Need Help With Run and Gun Audio

Hey all, need a bit of advice on my microphone set up. I'm a run-and-gun filmmaker. That phrase gets tossed around a lot, so I should clarify that for me it's not so much "walking around a city for a day and filming in a couple spots" but more like "skiing 100 miles across the Alaskan arctic over the course of 2 weeks in -20º weather." I only clarify because for me lightweight and portability are more important than for other styles of videography. My next project is two weeks sailing/hiking/camping in some remote fjords in Greenland during early winter.

That said, my current setup is functional, but not impressive. When I'm doing multi-cam and multi-talent shoots I use a Tentacle Track-E and Tentacle Sync for timecode jamming. It works great and records 32-bit float so there's a lot of potential, but I just use the stock Lav mic that came with the Tentacle system. I suspect there are several options that would sound significantly better with this setup.

When I'm trying to be faster (in the field and while editing) I use the DJI Mic 2 because it's just amazingly simple and easy. Again, I use the Tentacle Lav mic for this.

Question 1: Can you recommend a better lav mic that will improve the sound quality for both the Tentacle system and the DJI Mic 2 system? I've been looking at the Sanken Cos-11D but I'm curious to get your thoughts.

For on-camera audio I use the Deity D4-mini because I can have the shotgun audio and lav audio go to different channels so everything is recorded onto the video file. Obviously this is easy, but certainly not the best way to go.

I also have a Sennheiser MKE600 that I use as a boom mic for my home YouTube studio.

Question 2: What's the better solution? I'm sure I could get MUCH better sound quality out of a better supercardiod or hypercardiod mic into something like a Zoom F3, but I feel like that will be much too bulky for my workflow.

For things like travel YouTube I can probably get away with just a lav mic because atmospheric audio is less important, but it would be very nice to have. I know I'm preaching to the choir in this sub when I say that it would really elevate the quality. Is there a simple way to record both camera audio and lav audio simultaneously that isn't bulky (i.e., can more or less mount on the camera)?