On our 2004 T310SR, which has a 1,600# loaded tongue weight, I use the Barker Delux Hi power 3500 ball screw power jack. This is a very good jack. Since you have to lift the truck and the camper to hook up the WD hitch bars, use more jack capacity for longevity and still fit the camper ball coupler. This jack has an 18" lift. I always use a 6" wood block under it to raise the truck and camper high enough to hook up the WD bars.
Barker may be the few left anymore made in the USA, and it comes with a 2-year warranty.
See here: https://www.barkermfg.com/power-jacks.html
They also offer VIP 3500 or VIP 3000, which are ACME screw jacks in place of the ball screw, which are also very good, and a little lower cost. The VIP jacks have an option for 18" lift or 24" lift.
Shop the price; COVID and inflation have everything higher now. I looked quickly, and Amazon, if you have Prime for free shipping, maybe better than others. Just be careful to read which exact Jack part number you are getting; their description can be confusing. Amazon is hit and miss on the price out the door, so shop around for this.
The ball coupler on your T-267SR should accept the Barker jack tube. You can check yours; the Barker literature shows the VIP 3,000 jack has a 2" jack post, and the VIP 3,500 or the Hi Power Delux both have a 2 1/4" jack post.
I just checked 3 Sunlines in the barn that are in the same weight class as your T-276SR, and the hole in the bottom support plate welded to the frame is for a 2 1/4" nominal jack tube. The hole in the top ball coupler is a little bigger. You can check the bottom support plate with the jack in the tube if you have a caliper of some sort. Don't go by the jack foot or post that fits in the jack foot; it is smaller as it slides inside the outer jack tube that fits through the bottom frame support plate. The frame support plate is the choke point.
Your camper should have the same ball coupler as the other Sunline 8,600# GVWR-rated campers, and I have installed jacks on several of them. I suggest a 3,000# minimum; better is a 3,500# or higher-rated jack for your camper; again, that is not bigger than the 2 1/4" jack tube. This is where bigger is better as long as it fits in the hole in the ball coupler.
There are also a lot of other brands out there, many from offshore with different quality levels. And they may cost less than the Barker. If you are not going, Barker, ideally, find a buddy with a brand you choose with the same power rating and has had it a while to know it can last. I used to use the Atwood jack, which is also a very good jack, but they were sold to Lippert, who discontinued them.
I hope this helps, and let us know how you make out.