Looking over your new tire list and reviewing the Goodyear, here are some comments to consider.
On the Goodyear that had the blowout, I'm assuming you are referring to the Endurance trailer tire? If so, the ST22575R15 tires were in an E load range, with a Load index 117. Correct me if I have stated this wrong.
Here are some questions to ask yourself.
Something caused that tire to have a blowout; why? What is the DOT date code on the tires on the camper now? Assuming you bought all four simultaneously, they should be close. You are after the date of manufacture, not the date you installed them.
What tire pressure do you run those tires at?
Do you make a lot of hard 90 or 180 turns with the camper on a hard surface at your home/storage place every time you come and go to a campout?
Have you weighed the camper, axle by axle, and ideally, each wheel position?
What tire load range did Skyline place on the camper? With an 8,800 GVWR sounds like you already took a jump to E load range from what may have been a D load range by Skyline.
Comments on what may have happened.
There is a term called "interply shear" that happens on tandem axle trailers in turns. In a turn on a tandem or triple axle trailers, the tire tread and tire internals are getting stressed from the high friction between the road and the tire, when the tread does not slip on the road. The tire has to withstand this effect. Look this topic up on the web, it happens and is more aggravated by low air pressure, overloading, lots of hard turns, and tire age, to name a few.
Something caused your tire to blow out; think through what may have happened and why so you can correct it in the future. If you are low on pressure, that is a problem. The only way to lower the risk of interply shear that is practical, is more reserve load capacity per the loaded tire. This reserve capacity is above the stated rating on the tire. Some tire experts (I'm not one of them, but I had to deal with his) suggest 20% extra reserve tire capacity over the heaviest loaded wheel.
If you already jumped to E load range over the factory D load range, you could gain more reserve load capacity, but you will only get the increased reserve capacity from increased air pressure in the E load range tires. Suggest running them at the max cold side wall stated pressure on a trailer.
Was there a series of big potholes on a trip sometime? Potholes at 50 to 60 mph are bad news to a trailer tire, especially if the pressure is not at max. Damage internally can start that then takes a long time to rear its ugly head with a blowout.
There is a common trend on tandem or triple axle trailers when one tire blows out. The tires are at or close to or at full load capacity all the time. When the blowout happens, the other tires on that side go into overload. Now they have taken a hit of internal damage. It is common that those other tires can fail prematurely as time goes on. All of your fears about changing them now are a good concern. You are at increased risk if the damaged tires are not changed.
Having lived through the trailer damage that can occur when the tread flys off, the camper repair cost can outweigh the tire cost. Do you want the risk of simultaneously dealing with camper damage on top of new tire costs?
Not sure if you have a TPM (tire pressure monitor) on the camper; if not, consider adding one in the future.
I also noticed in your list of new tires; the Carlises were not at the 113 load index and not the 117 load index of the others. To give the Carlises a fighting chance, go with the 117 load index.
Try and figure out what caused your blowout and how to prevent it for the next time.
Hope this helps
John