You need more support for that stock! The single padded 2x4 is not enough, you need a big padded block or more of those padded 2x4s, maybe a frame of some sort....
C clamps have their use but not for this. To fit a barrel you need some support under the area you are working. Since this is a thinned down pre-carve it needs even more support.
Firstly check and make sure the stock is not flexing giving you a false read. Check it supported with no C lamps, they mat be flexing your stock. As said it needs more support.
Check this first!!! I'm going to be perfectly honest. What you have here is a pain in the butt. Why???
Normally the barrel is inlet to the stock unbreeched. Seldom if ever do you get a solid black channel, you are looking for good even contact but even with machine inlets a solid black channel is uhhh...unrealistic. You are looking for good even coverage. 50 percent even less but with good coverage.
Once the barrel is down the breech and tang are inlet.
With the barrel,breech and tang inlet then the lugs are fitted one at a time.
To simplify, steps A through D have been completed but it looks like step A may need to be revisited. What about B,C&D??? I think you can work around them instead re-doing them.
I'm not trying to make it harder but you are really to keep your head in the game.
For a good rifle the barrel must be fit well in 2 areas. The breech,the most critical and the muzzle. The muzzle is important but not as critical as the breech. I agree that there should be little to no gap under the barrel at the muzzle. So you need to bring the barrel down here some.
First, Clean out the lug inlet. Make sure it's not keeping the barrel up.
Lets read what we have here. There are obvious high spots in the barrel channel. The first about 2 inches behind the muzzle the other further back. Look at the sides. You don't want to remove material from the sides but you may need to clean out the corner where the side flat corners on the angled bottom flat.
Clear as mud? Just make sure the bottom of the side flat inlet is crisp and not keeping the barrel up.
You want to barrel channel to be a mirror image of the bottom of the barrel. You need good sharp chisels or at least one good 1/4 inch bench chisel, sharpened scary sharp. You can use other stuff like a riffler file or even an emory fingernail board but a chisel and a good one is whats best for this work IMHO. If you do not have one or know how to keep it sharp, get one, learn how to sharpen it and then come back to your work.
For this light precise work I'll scrape my chisel almost like a scraper. I'm not near as good as my mentor who goes to town with a bench chisel. I'm slow and conservative with it. For light stuff like this I will scrape with a chisel but for a little more bight, I'll work the chisel in the channel Flat side up. For me bevel up cuts too deep. Pay attention to grain. If it want's to chip or is grainy/stringy reverse direction as you are going against the grain. Putting a barrel in, I have seen the grain change 3 times in as many inches.
For here...
Check the lug inlet
Remove the high spots in the bottom of the channel.
Check and maybe cleanup the bottom corner of the side flat in the stock inlet not the barrel.
I'm sorry but another posters advice on filing the barrel flats was bad advice. You fit wood to metal not metal to wood especially in this case. With that said you may want to file and clean up the barrel lugs. It will not hurt at all to clean up the sides and round the corners of the lugs with a file. You really have good contact here. I do see some black in the lug inlet. Clean that out and make sure it's not keeping you up.
Remember what I said about good fitment at the breech and muzzle? In the middle, it's gravy. I would only remove material here to help with muzzle or even the breech. If the center of the channel is high it may be keeping you up at the muzzle.
You want to barrel channel to be a mirror image of the bottom of the barrel. I believe the lug may be keeping you up here. Remember what I said about the bottom corner of the side flat. I can't really tell but as always...
You want to barrel channel to be a mirror image of the bottom of the barrel. The big view we can see several high spots in the barrel channel. These and the lugs may be keeping you up. Whats not pictured is the breech. You need good contact there , especially on the breech face(the wood behind the barrel)
Good luck go slow It's just a matter of taking a little off here and there...fine tuning. It's looks to be really close.
Good Luck