It's all a learning experience Ty, and having Jeffrey's skill at the helm is a major advantage that you had. I think I'd have started off by making up the dunnage etc. to place the stove squarely over the front axle, and then packed around it. Non-load-equalising tandems are in any case, more stable than single axle, or load-equalising tandems. The main problem with them is getting equal tyre loads for tyre safety, rather than stability.
I owned a tandem a few years ago (rather like Jeffrey's) and never had any stability issues, even with a 3 tonne tractor on it, but I did find very early in the piece that I had to use 4 new LT tyres on it, at 80 psi, or it would throw tyre treads, and I'd then have an afternoon's work each time, repairing the mudguards. It started out on recapped car tyres, and it threw the first 2 treads (both on the rear axle) running completely unloaded at 80 km/h. Just the 790 kg the empty trailer weighed was too much for the original tyres. I've never had much enthusiasm for recaps, and after that it declined even further.