Does this combination work?

YES......good combo
Enjoy the memories to come.

What engine ? What transmission ?

I can not believe it has a 24,300 GCWR with only a 3.42 axle ratio. I would expect something like a 3.7 or even 4.1 axle.

I’m thinking of going with an Andersen Ultimate Fifth Wheel hitch to minimize weight in the bed. Would that be a good approach?

Check what your E rated tires' ratings are.
Most likely the two of them already have a combined rating of over your GAWR.
There's really no value in "over-rating" your tires when the GAWR is the real MAX rating you should be concerned with.

Thanks. I’m running E rated Goodyear Duratracs, but may upgrade to an F rated option.

“your truck's 10,000 pound GVWR is mostly based on dodging DOT laws”
“the rear GAWR is likely based on your tire capacity.”
“Your truck's payload is listed as 1,950. I'd guess...you will have a total of 3,300 pounds of "cargo" putting you over by 1,350 pounds.”

ONLY 1,350 over payload....he’s fine...not!

The trailer's listed hitch weight of 1,834 pounds is most certainly with an empty trailer and will go up as it is loaded. You will likely have nearly 20% of the traielr's GVWR as a hitch weight so I'd figure 2,400 pounds.
Your truck's payload is listed as 1,950. I'd guess your FW hitch will weigh at least 200 pounds. Add in your 700 pounds of passenger weight and you will have a total of 3,300 pounds of "cargo" putting you over by 1,350 pounds. So, if you think you need to stay withing the truck's GVWR then no, it won't work.
However, your truck's 10,000 pound GVWR is mostly based on dodging DOT laws that kick in above 10,000 pounds. Weigh your truck. See how much weight is on your rear axle. If you can add 3,300 pounds to the rear axle weight and not be exceeding the 6,500 pound rear GAWR then you should be fine. Even then, the rear GAWR is likely based on your tire capacity. If you can upgrade your tires to higher capacity then you should be able to haul more weight.
Lots of people will argue all day long about this because they think a truck's GVWR is gospel and going 100 pounds over it will cause all sorts of mayhem and carnage. When you start to look at the ratings of various components and understand how they work together you can usually find a way to make it work.

Yes, it is possible due to having a 6,500 RAWR and a 3,095 current wt on rear axle. This means that you can still add 3,400 to rear axle wt before going over. You do realize other things in truck, truck bed, etc will take away some of the 3,400, but still room for approx 24-2500 in actual pin wt of FW.

Jerry