You might try 3-4 coats of dark brown paste wax as a finish.... yes it would need to be refreshed over time but it would likely give that non-uniform look. A wax finish was common on relatively rustic furniture in past centuries... (i.e., not fine furniture).
If you skip the bread board ends you could resaw the 4th board and use it to veneer glued up pine to create the legs and stretchers. By tennoning the long stretcher and putting it into a mortise, instead of having it lap over the short stretchers, you would hide all the ends. By doing this all the wood in the table would match, it would take the finish the same, and it would save you from having to match "new" wood to "old" wood.