Since your stock appear too light, even after repeated staining with an organic – coffee, berry juice, etc – then you may wish to check locally for some sort of enterprise that finishes wood. I would guess that sounds a lot easier than the actuality. However, if you could eventually find a good oil based stain somewhere, or an art supply joint with assorted earth/oil based artists pigments in the umbers [wood colors] you'd be happy, no doubt. Since you've prob'ly already done that due diligence, stains also can be water borne [what you're using] or alcohol soluble. So, what dissolves in alcky, besides livers? Well, quite a few organic substances, as also with water.
But, sometimes the alky leaches out more/darker color from the dye-source. If it's applied rapidly/evenly, in such a manner that you don't wipe it off as fast as it penetrates, you can get more saturation than with the same substance in water. Another way to intensify color is to heat the liquid – – and boil out some color from whatever nut, berry, etc y'r trying to turn into stain. [a glass jar with a loose lid and direct sunshine can get pretty warm, also – outside for flammables, please] Also, you can concentrate the color by reduction with boiling. That might work with the coffee.
Mostly, however y'r looking for a brown of some sort. And brown has black in it. And asphalt is black and common and mineral spirits/paint thinner soluble. So think in layers of application. Since the linseed oil is mineral-spirit solvent based, some asphalt saturated turps or spirit’s can be added to y'r stain layers on the wood. All going thin-coats & slowly,of course. But such efforts can be washed off and tried again – one of the 'secrets to getting what you want – as each 'tidal flow' leaves some color until it's where you want.
Now, the asphalt will also go into the linseed oil thinner. Or, just some of the oil, if the mix is set in sun and baked for a bit. Not too much, and stir it well. And make it lighter in color than you want, too. You can always add more thin coats, but get it too dark and streaky, and it's wash it off and start again. However, pure linseed does not cure well, except in really thin coats, well rubbed in let to cure in the sun. The finishers trick with linseed is to add a bit of cobalt dryer from the painter or artists supply joint. Since that's a long shot for you, if you can find clear wood varnish, that smells like paint thinner and gets sticky when you rub a drop of it between y'r fingers, then add a bit to the linseed rub-in, and presto, you have a bit of cobalt dryer in the mix. Better film forming properties, too. And a durable finish, to boot.
The reason us gunnies used and loved linseed is because it's cheap and simple, if somewhat short on performance and durability. But, it's easy to touch up and re-new, each coat getting older and mellower. And, all the old gunsmith books had recipes revolving around the stuff. It just take patience to get a fair film of it on wood -- and determination. Today, we know that harder resins and better chemistry has given us easy remedies to fill up that word and make it purty.
Hope something of this works for y'r present project. In your travels, keep an eye peeled for a sigh-painter's shop, or anywhere wood might be finished. Such products are pretty standard fare around a good sized population that supports a monied class, somewhere's about. Could be you may stumble upon an unexpected source for goodies. Would be interested to hear of it. Happy oiling.