Take a serious look at the differences between 60's and 70's trailers, and you might find enough to recommend the 70's trailers that not having an Alclad mirror polished skin is worth the trade. You might also look through some of the threads in the "polishing" section of the site, and you might see some examples of just how shiny a 70's era trailer can get. A good compromise might be a 1969--they had the body style of the 70's trailers, but were still made of 2024 T3 Alclad (but they didn't have center baths). Because they were a transition year, though, be wary that some of the parts on those trailers are unique to that year, and hard/expensive to find.
I chose a 70's era trailer because I thought I could get a factory installed grey tank (ended up buying too early in the 70's, though), plus the body is a little wider, and there are more windows, which gives the trailer more light and a more "airy" feel. I felt closterphobic in most of the 60's era trailers I walked into.
In terms of changing the layout, anything is possible with enough time and money. Just be aware up front that making massive changes to the layout will mean developing skills you didn't know you need. There is an access door for the back of the fridge, a chimney for the same, a fan vent over the stove, inlet/outlets for the furnace, a large hole where the hot water heater is installed, black and grey water vet stacks, and an inlet for filling the fresh water tank. The water lines are up inside the trailer, but the drainage plumbing is mostly under the floor. Anything that you move requires patching holes and cutting new ones.
I considered moving the bath around in my little trailer. I had already done a shell-off to replace the rotten subfloor, repair the frame, install grey tanks under the floor, and put on a new bellypan. As I considered moving my bathroom around, I ran into lots of appliances that would make the move difficult, for example, I would have had to move my water heater (which sits in a roughly 15x15 square hole in the shell) to another location, meaning I would have to patch up one big hole, and create another. My then proposed shower stall would have occupied almost half of a long window, which would just end up looking jury-rigged (not to mention making it hard to open the window). The wheel wells get in the way of side oriented bathrooms, but can be worked around. Of course, the longer the trailer, the more flexibility you will have in making moves.
When I was hunting for a trailer, I saw many that had already been gutted, and I thought that might be the way to go, since I intended to to a full refurb of the interior anyhow. In retrospect, though, I am glad that I bought a trailer that was pretty much complete, just so I could really see how all the puzzle pieces fit together in the original build. I am now in the process of reassembling my trailer, and it will end up laid out pretty much the way it originally was. I find myself taking the old pieces out and trying to recreate the way things were layered in so that I don't end up making a mistake, and having to disassemble stuff to redo it.
Not trying to discourage your interest in a completely new layout, just hoping to help you manage your expectations (ie., this is a massive overhaul).