Hey Bowtie76,
Welcome. Glad you are here. That looks like a pretty darn nice Cargo Trailer, and a very useful size 7 x14 x 7. I am right at 6' tall, but so is my trailer. 6 x 12 x 6. Another 1' or even 6" would be very nice, but it is what it is... for now. I also built mine as Toy Hauler/ Camper, and I have a couple bikes as well. I go to the rallies at Sturgis and the Iron Horse bike rally and Rodeo and we do poker runs and try to do charity, for the children and vets. Finding a hotel room during the rally is impossible, even a year in advance. Plus, the winters are very long here so you have to get in all you can when the weather is nice. So the camper has been a perfect solution for me. I know you will love yours as well.
Ok then, let's talk about you. Having a sport or hobby that you can enjoy with kids is priceless. Time goes by really fast so enjoy them all you can. It won't be long before they won't have time for you. That looks like a pretty good helper you got there.
Cutting sheet insulation. Lots of ways to skin that cat but you really will need to set up a rip fence to get consistent, straight, relatively precise cuts. You can use a table saw or even a circular saw, just turn the blade around to the wrong position and it wont throw all the shavings. Also the oscillating multi tools work well, and even a sabre or jig saw. I have seen people cut foam with a hot wire set up and razor knifes work also. Just score the line on one side and bend to snap it then cut through the other side like drywall. Hopefully, you will have a majority of the wall insulation that is the same size, like 15in wide x 7ft and you can just knock out a pile of those in a hurry. If you have some gaps just fill them with canned spray foam. Try to get a couple of inches of insulation in the ceiling and a couple inches under the floor. It will make a big difference in comfort and your ability to heat / cool the trailer and helps with noise as well.
All kinds of different ways to deal with the bed as well. You might want to consider a metal frame to save the height and keep the mattress in place when lifted. Then you can use 1 1/2" or 2" tube instead of 2x4 lumber. I'm not sure what your lift system is like, but I would try to anchor into the wall studs at the top as opposed to the roof spars. You can use "Rivnuts" and just drill into one side of the stud tubing. They insert into a predrilled hole and then mushroom out when you tighten them down. Then you can use bolts or eyebolts or whatever you need to attach the cables. Here is a link to an example of rivnuts or nutserts. I also used them to mount my awning to the wall studs. They are pretty awesome and very strong.
https://img.fastenal.com/catalog_pages/2013/01-300.pdfOk. That's all the damage I can do for one day.
Good luck and keep us posted.
McDave