OK

26 " barrels on this is about the same as 24" on a bolt gun. The .500 at the muzzle is not rediculous a lot of bolt guns are .600+.
I agree with Marrakai and others that it is not ideal, but then this is to be a cheep fun rifle I presume and not a masterpiece so I would not waste the time and money turning them down.
In any event people are only suggesting slimming them from the monoblock forward so you don't need to change that dimension. However are going to need a taper turning attachment and some considerible knowledge to set it up or it will cost you money to have it done.
I would leave well alone.

Pull the barrels check the soldering and reassemble.

As to strength I have done the sums and on CIP Piezo data ( 47,000 and 46,000 psi )and Lyman cartridge blueprints then the 30-40 works out at 4.89 long tons breach thrust and the 30-30 4.12 long tons breach thrust.
We do not have LC Smith actions, is this a 2 3/4" 16 gauge.? If so you are not a mile over that with the 30-30/30-40.

I would do the following to test it.

With all of the usual disclaimers etc.!!!

Find a max load in a reputible data book with the slowest non compressed powder. load 6 of that load with a bullet weighing 10% more than listed ie for a 170 grain load, use a 190 grain bullet.
Measure gun accuratly particualy any clearence on the bed and the action face. Put gun in a fixture. retire behind a wall with long peice of string, no don't just crouch down. Fire 3 left and rights and then re-measure. That 10% extra weight in the bullet approximates what the continentals do/did for proof.

Or

Load a max listed load and liberaly oil the cartridges before chambering them. What the British proof house did/does.

No it isent perfect science, but it is about the best you can do without expensive equiptment.

Re-measure and if all is as before and the gun is still tight, you can proceed to finish the gun.
If it moves even a fraction, then pull the barrels and bin the action. Please do not be tempted by the "its only 2 thou" If that action is no good and you want to continue I personaly would buy a 16 guage Baiakal and monoblock that, they are as tough as nails.

I would regulate it with a nice mid range load so as not to stress the gun over its lifetime. ie 30-30 170 grains @ 2100 fps 30-40 220 @ 2000 fps. I would personaly find a good quality (win, rem, fed) factory load in the mid range and regulate with that.

You will not make a silk purse out of it, but you can with diligence to the finishing have a usefull fun rifle, that will not disgrace you to show and provide years of interesting fun shooting.

All of the above is only my personal opinion based on what has gone before and not general recomendations in all circumstances, but I hope this helps.

Regards