GaryR, French Polish relies on the pressure of your stroke to lay the finish onto the wood. In this case you must lay the finish onto the wood without using pressure. Pressure/friction allows the "grain" applied to be removed. I have been using Pro Custom Oil now for more than 15 years. With the liquid Pro Custom Oil, one uses a soft cloth dampen with finish just as an applicator/hand brush. By a light dragging touch you lay about a .05-1 Mil finish onto the wood. Just enough to put a layer of finish over your work. Let it dry completely. Apply two/three coats and then level sand.
With the spray can Pro Custom oil you can do more/faster as the can puts on a better layer that doesn't run as fast as the liquid does. It is a balancing act to get the finish and the material painted on to lay flat. There is a lot of level sanding to be done between coats so the final finish lays flat. The sheen of the final look may be adjusted after the finish is leveled. In this case the original finish was a full gloss oil finish from another English restoration earlier. I use Pro Custom because it allows me to replicate most finish looks generated over the years by all of the different companies. It can go from an in the wood low sheen to Weatherby gloss with some elbow grease and polishing.
I use Acra-glass liquid for my gluing most of the time. However on this project I needed to make sure it held very well and through different climates. Epoxy holds but the two different woods move. That gives the glue line a chance to come back later. I used Elmer's Wood glue this time. It has a better chance of holding during climate changes. The original hide glues are the best for this application. You can still buy horse hide glue in flake form and make your own. The glue has a short pot life ,so you only make up what you need at the time. Make sure of your ventilation too...it stinks. I have taken on restorations that are very old stocks which are repaired with this type of glue. They held up until I put the Acetone bath to the wood in an attempt to remove the oil soaked into it.