Gum benzoin is easy to deal with. It is very soluble in alcohol. All you need to do is grind it to a powder (or hammer it, which is how I did it because my wife won’t let me borrow her mortar and pestle), then dissolve it in alcohol. Then you can easily strain out the sticks and dirt and pour the clean solution into cold BLO. Next, heat the oil to drive off the alcohol. Alcohol boils at about 200 F.
Gum rosin can be handled the same way. It is soluble in turpentine and alcohol.
I made a batch of varnish last summer using this method. I heated it to about 240 degrees so that the temperature was above the melt point of the rosin and gum benzoin. I don’t know if this is really necessary or not. It could be sufficient just to have them in solution, but since all the recipes I’ve seen involve melting the resins, I thought that would be the safest way to go.
I ended up with a nice low gloss varnish that seems to be durable. I put a couple of good dents in my gun this fall,, and the varnish didn’t crack or chip.
I ALMOST did this very thing a few months ago, but was scared of heating alcohol. I dissolved a quantity of benzoine in alcohol, filtered the sticks and bugs out of it and poured it into aluminum cake pans to dry. EVENTUALLY it dried out, but I had a surprising amount of loss (by weight) of the benzoine, which is alright, I guess, since benzoine is a lot cheaper than mastic!! I then put the dry benzoine in the oil. It was a lot of trouble this way. I had to wait weeks for the benzoine to fully dry (or nearly fully dry...)
My rosin has all been quite clean, and it dissolves readily into the hot oil, as does mastic, which is why I have just stuck with those two. They were commonly used at the time for "plain brown varnishes". Mastic ain't cheap, though.
Actually, some of the varnish I am currently using is some I did with rosin and the benzoine. I'm not really convinced the type of resin used makes a whole lot of difference, other than rosin is supposed to eventually get brittle. Mastic is considered one of the better resins, and it is known as being quite elastic (hence the name...you can chew mastic. Chewing gum is, or at least used to be, made from mastic).
I'm not a chemist, I'm an alchemist.