Or..a standard poe injector and customize the rj45 arrangement swapping the appropriate wires... correct?

Yes that's true, that's the other option.

I wanted my Starlink to run off 12v so that I didn't have to depend on my inverter to power the Dishy router. I purchased the three items to make that conversion from Amazon along with a router that would run on 12v and it's worked amazing. I get speeds well into the 175 Mbps range or higher when we are camping in the middle of nowhere in CO. The components are the 48V power supply, the PoE Injector, and the Dishy Ethernet adapter. I also wired all my equipment into my front storage compartment with everything else so that it's easy to diagnose and see what's going on. We have very strong signals throughout the camper and a decent distance away. Works great and was super easy. I also added a bank of switches in my basement storage compartment to power the router and the dishy.

Thanks for the feedback COReflection, I was leaning towards using those exact components . Glad to hear they work well.
I'll probably skip the adapter, but it's the other two components that are the important ones. What is the little thingamajig above your adapter?

Sure--no problem.

The first pic is the Ethernet Dishy cable plug-in where the dishy plugs in. The second pic shows the PoE Injector on the top and then the 48v power supply on the bottom. Fourth pic shows the shelf that I made and mounted in my front storage compartment and fastened the router. I'm an IT and Cyber guy and was going to cut the Ethernet cable and change the plug end but decided to keep it as clean and OEM as possible so I ordered the cable adapter for the dishy. I didn't know if I would ever want or need to use the old Starlink router again too but found it to be way too big, bulky, and heavy so it stays home now.

I believe it's T-568B pinout

The data is, but the POE is nonstandard. You can either move the pins around so that when you plug into a standard POE injector it puts the power on the pins Starlink needs, or you get a custom injector that powers those pins when they are located in a T-568B location. Either method works, but it can get confusing. I terminated mine standard T-568B, and used a custom injector, but the method Scott mentioned works as well.

You would want to keep that cable well marked.....

I've got no input for the starlink setup as I don't own one. What others mentioned about sticking to 12v does make sense with the size system you are proposing. I do disagree with some of the #s mentioned above concerning what to expect in the way of power from a 300 watt system. Basically you can expect about 30 amp hours from each 100 watt panel per sunny day and no shading. I like to use amp hours because it makes calculating usage and storage easy. You mentioned a 100 amp hour battery where all the power will be available. So, on a good day it should be able to be brought up to full. Keep in mind, that won't happen in the fall and winter. You'll have to also keep that battery at whatever it's min temp is to charge, as well. Also, that size battery bank and system may give you nothing extra for cloudy days, but you have a generator. You still have to figure out what you expect your daily usage would be to see if that's enough.

Just a data point for you. I have an off grid cabin with 960 watts on the roof and 8 x gc2 lead acid batteries for a total of 860 amp hours at 24 V, so 430 amp hours of that as available. I have a 3000 watt inverter, and run 120v power underground to the cabin. The panels and all the solar equipment is in / on a shed in a field and cabin is in the woods, so it was easier to deal with distance and wiring losses by going to ac for the run. Cabin has a sureflow water pump, microwave, tv and a 10.2 cubic foot big box store fridge (it is surprisingly efficient and much cheaper than installing a dedicated solar fridge when panels are so cheap), as well as 120v led lighting, ceiling fans, and the charging of all our electronics and laptops. Stove is propane, but plugs in for piezo lighters, and when you use the oven a glow plug thing runs consonantly to start the flame while it cycles. I don't spend winters there, but in the fall, I do have to run the generator to charge the bank if we have several days of cloudy weather. It's located in central NY, so we get more sun than you do up there.

The setup you're proposing is similar to some solar systems I've installed on boats, and should work well so long as you can deal with its limitations. If you do go with an inverter, I would suggest going to a 24v system unless you're just planning on a very small one. I would also leave some room for growth in the electronics you buy in case you want to double your storage or panels in the future.

For sure. I am pretty sure POE negotiates, so it should not apply power unless everything lines up but I would not want to risk it. Like I say, I prefer terminating to the standard and using the injector to deal with the nonstandard. Easier to remember to not plug regular things into my injector than to not plug my dish cable into something else.