Big breath, not the end of the world. It's an easy fix. First, lets play this out to put it into perspective. You have action made by X, stock made by Y, and floormetal made by Z. I'd bet a paycheck none of these manufacturers talk to one another in any meaningful capacity to ensure component compatibility.
This is where guys like your smith, me, and others come in. The tribal knowledge is what you pay for. . .
As for your gun:
Insert the magazine with a cartridge in it. Have the bolt removed. Look down the ass end of the receiver. You should be able to barely see the top edge of the primer pocket. If we image this the circle of the primer is tangent to the receiver bore. It basically forms an upside down figure "8". If you have/see this its a good thing. It means you have enough case overlap with the bolt so it'll run properly.
Now, the magazine won't catch right? Chances are the action was bedded a pinch too deep or the floormetal is sunk a little too far into the stock. There's a very, very easy way to fix this. It's not my choice, but if you have zero tools/ability its the path of least resistance.
Hardware store, shim washers. Make sure they are at least 1/2" in diameter on the outside and will fit a 1/4" screw. Stack between floor metal and pillar till it works. Double check the case overlap and do a feeding test. If it works, your all set.
Another way:
If you have some tools, just remove the magazine release lever and grind a smidge off of it. Chances are the magazine is shoved into the bottom of the action. Removing a pinch of material from the lever will effectively drop it so that it can register into the "louver" feature on the back of the box that retains it. If you go this route, SMALL MOVES. It's easy to get carried away. Also pay attention to the geometry. It matters. You want it to catch and hold, not pop loose under recoil or get stuck because it acts like a porcupine quill. Some will suggest its better to work on the magazine. I disagree. The AI's, ARC's, Accurates, etc are all pretty good. They do a good job of controlling that feature. The gun is the problem, not the box. Don't create a cascading effect.
One last thing:
With bolt removed look down the back end again. Pay attention to the raceways that track on the bolt lugs. Are they on the showline? Meaning half in the stock, half out of the stock? Just look and trust you eyes. You'll be able to tell very quickly. Reading your post again it suggests that if you really are .125" short (1/8") of being able to insert/register a magazine, then the action is either bedded far, far too deep or the floor metal is sunk too far into the inlet on the bottom.
FWIW: Most pillars on guns set up like this end up with the front pillar being around .725" in overall length and the rear is 1.075". There is some fudge room built into this, although not a lot. Again, if you are a legit 1/8" short then someone goofed up. That's going to require a lot of washers to resolve. Either way, do the washer trick if for no other reason than proofing out the problem. It harms nothing and gives you a direction.
Good luck.
C.