In my opinion, the best bet would be to have something like a solar panel or a water mill feeding into a system for nitrogen fixation.
If you can get enough energy to convert nitrogen to plasma (something like 900~ joules?) than you can "fixate" the nitrogen in the air into NO2. If you can bubble this into water, it will slowly generate nitric acid.
It's a somewhat long process, but it's probably one of the best overall processes for making nitrates that you can do on the small to medium scale.
I've investigated it quite a bit and plenty of hobbyists have done it, but it does take specialty equipment.
If you want to really do something low tech, then I think you're on the right track with the farm style nitre beds. I don't know much about making nitrates or explosives out of the very very common chemicals, but nitrogen fixation was the standard method of industrial production for quite some time. It is very energy intensive, but can also be very cheap as well once setup properly.
Although, this reminds me…..
If you could get ahold of a whipped cream maker with the commercial whipped cream canisters, or even the simple grocery store whipped cream spray cans, you could maybe make a panclastite by intentionally condensing the N2O that they use in that sort of thing.
If you can get it liquid it would make very potent explosives if mixed with fine saw dust or paper, but they would be very sensitive.
Lead styphnate seems as though it would be very very hard to make without quite a solid industrial base or a way to source resorcinol.
You might be better off trying out something more like lead picrate or lead azide.