I agree with everything Joel has said on this.
About your questions as to what you should do next, I think bedding is about the only thing I would advise. The other work you mentioned about lapping lugs and truing things will change headspace slightly. That would require a little bit of barrel work and I don't believe it's worth it to spend money for a smith to work on a factory barrel. I always advise customers to save that money and just shoot it until they're ready to pay for a new barrel. It will need one someday anyway and it's a much better investment. It's what really makes the biggest difference in a rifle anyway.
I would put the barreled action in the stock and carefully trace around the tang with a very sharp pencil. Then use a dremel to rough up the surface areas in the stock bed area obviously staying inside of the traced line around the tang. Leave no factory paint remaining and leave it rough. This will probably allow the barrel to sit straight down the channel.
Wrap some layers of tape around the action screws so they fit kind of snug inside of the pillars, not real tight, just kind of snug. Trim that tape off at or just below where the screw sticks out of the pillar. I use seperate, shorter screws for this. You can get them at the hardware store (they're 1/4X28) and trim them to length. This will keep the screws centered in the pillars and keeps excess epoxy from getting all over the screws and into the pillar.
Put the screws through the pillars and screw them into the receiver then see if it will fit into the stock. If it fits with no problem it's ready to bed.
Put a layer of masking tape on the front, sides and bottom of the recoil lug for clearance later. Trim tight with an Exacto blade. It might not be a bad idea to put a few layers of tape around the barrel out at the end of the fore end, but not enough to where the barrel fits tight and not so much as to force it into center if it doesn't want to go there. If it wants to sit a little off center then let it do that and sand out the channel later as Joel said. It's important to make sure the barreled action sits completely relaxed and stress free as it cures.
Remove those pillars and apply release agent to the action and screws then put them back on and bed it. Try to smooth it all out so that you reduce the air bubbles. Spread it on the sides of the pillars too. Once you squeeze it down into the stock, look to see if the pillars are flat or even better slightly protruding down on the bottom side of the stock. You'll want to make sure that the bottom metal makes contact with the bottom of the pillars. If they don't, unscrew them one at a time and put a small washer in there then gently tighten the screws so it pulls the action and pillars down. Once you feel it snug from the pillar making contact with the washer stop. No need to gorilla torque it.
I'm sorry for rambling I realize that's WAY more than you asked for but I'd bet if you do that it will shoot noticeably better.
Marc