I would brown the barrel rather than bluing it. Laurel Mountain Forge Browning solution, available from Track of the Wolf, works very well and does not require the careful handling some others do. It also degreases the barrel when it is applied but I would do that before I use it, in spite of the advertising. I have used the product a lot. It is important to draw file a smooth surface on the barrel before beginning bluing. Also, humidity helps. If you live in the south west, for example, browning and bluing, absent some humidity, can turn out poorly or take more time than in the humid south. John Bivins had a plan for a sort of "damp box" to be used for barrel finishing which was simply a tight wooden box - with a door of course - with provision to hang a barrel, a large light bulb and a pan of water near it. That created enough humidity for an even finish - browning and bluing are both controlled rusting processes.
One thing to keep in mind when building any pre-inlet kit is that CVA kits and others like them are mass-produced, unlike kits from Jim Chambers. If the worker doing the inletting is off a bit or the router bites too deeply, it is often difficult to correct. I learned that the hard way 42 years ago with a Numrich Arms half-stock rifle kit and I have an unfinished CVA kit which also had those problems - rifle rather than pistol. You have been advised to go slow already and that was very good advice. Also, don't leave a lot of unnecessary wood on the stock but leave enough for strength in the area around the barrel, lock and breech. Leaving too much wood is a common problem with first-time kit builders.
Good luck with your build and post some photos when it is done.