I won't proclaim to be an expert, but here's what I would do.
Make some cross cuts at what you perceive to be the most damaged areas. Now make a few other cross cuts at what appears to be the least damaged areas. Using an awl poke and dig top, sides and cut side (probably end grain). Also test a few random areas at what appears to be non-damaged surfaces that have been at least 18" above the floor and as far away as possible from walls, ceiling, windows and doors. Good stock may be just slightly softer at the fresh cut end grain. Well dried stock should not have that much deviation in softness. Try the same test using a known well dried piece of lumber you think is the same species. This is a general dry rot test. If it's rotten it will be soft and easy to push the awl deep into the wood and will crumble if scraped.
Within the cuts look for color variations, mold, fungus, water stains, etc.. Try planing or sanding down a section that is discolored and see how deep the stain continues.
Good wood especially old growth mahogany can be exposed to moisture for many years without failing. Look at some old boats.
Cut off the worst sections and discard or try and plane down to a good surface. Brush off any fungus, wipe down with an anti-fungal (only if you really think you need it, they often will discolor the wood). Sticker and stack as if it was freshly milled wet wood. Start of stack should be at least 18" above ground. There should be air gaps between sides of each board and stickers between each layer. The entire stack should have preferably 18" of clear space around all sides, top and bottom. If possible have a fan to circulate the air.
I hauled away a junk mahogany and teak boat and recovered well over 70% of the wood. Essentially free wood except of course for quite a bit of labor involved in reclamation. I still have a few pieces and I feel it is of higher quality than many of the young new-growth mahoganies being sold today. The teak was near perfect after re-surfacing. Plus it can be a sales point. Many of the yuppies prefer to purchase items made from recovered product like fences, barns, broken furniture, etc..
I have the luxury of not having to warehouse purchased exotics with recovered wood. I would keep a careful check on the drying condition and possible contamination if I needed to mix expensive stock with recovered stock. I have not yet had a problem with cross contamination from trees recovered from the ground or other mold and stain issues. I have however rejected wood/trees that appeared too rotten to recover enough to be cost effective. I am more concerned about possible termite and beetle transfer in my sheds, although I haven't had that problem yet.
The wood in your pictures doesn't appear to be that damaged but I would go on feel (above awl test, and cut density) rather than sight.