Hi LittleA -- Hope you're enjoying the Forums!
Airstream's weights pdf page
shows a 3950 curb weight for the '65 Overlander without options (eg, was an air conditioner standard or optional). Do you know what the weight of your gutted trailer might be? The difference between curb weight and gutted weight is going to be a prudent amount of cabinetry you can put back into the trailer. It's amazing how light the original-build compartments and furniture were. 1/2" ply for cabinetry isn't going to work out well unless you re-do axles and really look at all frame issues.
Unfortunately for this discussion, Airstream's page doesn't give GVWR limits for the mid-60s. Do you have a manual that shows that? I'd guess a payload of 700# plus or minus how much?
Putting a stove in the front will contribute more to tongue weight. That could be handled with some thought. I definitely wouldn't put anything heavy at the back of the trailer. The distance from the axles to a heavy object at back can get to be a long moment
arm that could be very damaging going over normal road irregularities. This is why bicycles mounted on the back bumper isn't a good idea.