We had some luck with alum as a pre-mordant on wool, reportedly tin works as well (for a somewhat different color). The base color was a bit more dark orange (or something .. my "color naming" capability makes LOML cringe).
I can't say we've used the wool long enough to make a strong statement of how colorfast it is, but the literature indicates its quite good.
This mostly mirrors our experience, although our alum mordanted one wasn't quite that dark.. I think we might not have used enough osage... maybe..
I've been wanting to try logwood as well but haven't had time.
Another dye we recently tried (so again a bit early for colorfast statements... ask me in 20 years LOL) is chestnut hulls (the outer burrs not the nut covers). Without any mordant that gave a really nice golden color. I've put the sample through two washings and so far so good. I have a large box we collected of these so we're intending to try that with some other mordants and see how it goes come spring (my last-fall project was re-vamping the old hot-tub gazeebo into a dye studio).
The problem with trying to dye wood is that cellulose doesn't uptake color the same way as protein fibers. I think you can get some colors but our experiments with cotton (as a vaguely close proxy) has been that it both lacks color fastness and doesn't take color nearly as well. I suspect ~most~ dyes that work on cellulose will work on wood.. There may be some cases where you can use other things as a stain with a top coat to protect it.. again not sure on how stable the colors will be there.
We haven't tried the lichen dyes on cotton yet.. the lichen dyes are pretty significantly different in behaviour than most natural dyes so they're pretty exciting to play with. In particular some of them are ammonia extraction and give (colorfast!!) bright reds and purples which are REALLY hard to get with most natural dyes. The downside is that the ammonia extraction takes several months and requires shaking the jars several times per day. So we'll have some more data on the couple we have in progress by sometime in the spring.