I have used a "modified' Walker method for a number of years now.
It's just not rocket science. I have used this "from the muzzle" method quite successfully - as witnessed by the patterning paper after the choke opening. The "from the breech" method is much more professional and mistake-proof, but the "from the muzzle method" can be used successfully IF YOU ARE CAREFUL AND TAKE IT EASY. Once metal is cut and gone, IT'S GONE. Think a lot before you cut. I suppose it would be possible to do the job without my Skeet's Bore Gauge, but it would involve quite a bit more travel to/from the range to confirm how much I had opened the choke after each metal removal session. Much easier to use a device such as my Skeet's Bore Gauge to measure (in thousands of an inch) how much metal has been removed.
I figured immediately on reading Walker's article that his having the work initially held horizontally was bass-akwards, as it would seem to introduce a whole bunch of inaccuracy in trying to keep the cutting tool parallel with the bore.
I hold the barrels vertically in a padded vise, muzzles up for the entire process. Keep in mind that SxS shotgun bores are NOT parallel. Each bore must be plumb up and down in the vise. I use a LARGE T-handle, at just below eye level, to drive the expandable reamer, and ENSURE the T-handle is as horizontal as I can eye-ball it. I let the weight of the T-handle and the reamer control the "rate of feed". I keep the expandable reamer well lubricated, and withdraw and clean the cut metal bits from the reamer's cutting edges (with toilet paper and a jeweler's screwdriver) and then re-lubricate, and repeat the process. I only rotate the reamer several half turns then withdraw, clean and relube. Then re-measure with your bore gauge. Repeat the process as required. As I'm a hobby-gunsmith and RETIRED, I can afford the time to nibble away at the job - a gunsmithing business could not afford the time to do it my way.
When the desired diameter is achieved, I change the barrels in the vise to horizontal, to remove the cutting tool marks with a brake hone (if necessary), then polish with a flex-hone.
Those shotguns with a parallel length forward of the choke will guide the reamer straight down to the choke with no problem. Those shotguns with chokes that are a simple cone toward the muzzle require that you PAY A LOT OF ATTENTION TO KEEPING EVERYTHING PLUMB AND THE T-HANDLE PERFECTLY HORIZONTAL.
I guarentee nothing - except that this modified Walker method has worked many times for me. I work on my shotguns to PLEASE ME. I do not voluntarily work on other folk's shotguns - but I have had my arm twisted several times.
I found that the metal in my Fox, Parker and LC Smith guns all cut reasonably easily. My Browning Superposeds had much different metal in the barrels and took some effort.
I don't recommend this method to other people, but offer this information FWIW, as it is what I have done, and it has worked for me.