I run Starlink but only for about two hours a day because if how much power it eats. But I haven't done the 12V conversion so I have to run the starlink and my inverter for it to run. If you are looking to get star link - look at the new mini - much better than my old system.
My experience with V2, V3, and Mini Starlink is that there is little power to be saved by only going to DC. Most of the "excess" power they use is in their modems. If you use your own modem, the power usage does drop.
I'm ignoring the inverter efficiency part because that depends on the specific inverter and how it is used. If you are using a 3kW inverter just to run Starlink only, then there is power to be saved going DC. If your large inverter is on anyway for other things, then no power to be saved. If the Starlink is powered by a little 300W portable inverter, then no power is saved going DC until the SL modem is replaced with one's own.
For example, our V2 average power usage dropped from 60W to 45W going from original setup running off a 300W inverter to using a DC POE converter and our boat router.
There is little power to be saved operating the Mini on DC because it already operates on DC. However, connecting it directly to DC is much more convenient and gets rid of the inverter. Ours uses 22W on average. I have not yet bypassed its modem to determine if there is any power to be saved there, but it is a pretty small and weak modem, so don't think there will be savings - just convenience.
My solar panel is about a 380 amp panel - it usually is putting out in the.mid 200 amp range, or less. I think I've seen a couple days where it was putting out a bit over 300 amps. I have twin alternators that will put out 240 amps, but I throttle them back to 80% output. I think if I had more room in my engine compartment I would put in two much higher output alternators such that I could fully recharge I say 15 minutes rather than the two hours i currently need and then drop the solar panel.
Did you mean 20/30A solar output from your 380W panel, or 200/300Ah/day from them?
It will not be possible to recharge in 15min using larger alternators. The batteries won't (should not) take that much current, and it is unlikely 1200A of alternator output can be connected to the types of engines on most boats.
Mark