The linseed oil has made changing the color more challenging than it needs to be. It is done.
I would use dye stains.
https://laurelmountainforge.com/stain.htmI'd get the black one, the red one and a brown one.
Strip off all the linseed you can with a solvent. Lacquer thinner, acetone, automotive finishing degreaser, use what you have.
Use the stain by diluting it and making many passes. Adjust he color as you proceed.
The real Hawken pictured looks to have used color in the varnish. You can tint varnish with the dye stains above. There will be a learning curve and test pieces.
You can add bone black to your finish to get the old timie black look too. It may take many coats.
Stop using linseed oil if you want it to like like the Hawken pictured.