I don't have the Speer 14, but do have a #13 at my office. So... What you'll learn about the .357mag, vs. the .38spcl+P and .38spcl, is typically, the same loads will work in the mag case, at nearly the same pressure as the Special case, if you simply add 10% to the .38spcl or +P charge weights. As you're seeing, most load manuals don't show "light loads" or .38spcl level loads for the .357mag data, simply because they know you can use the 10% rule of thumb and apply their .38spcl data, or know you'd simply use a .38spcl case instead of burning an extra 10% in powder.
So if you turn back in your #14, I can't imagine it won't have the same powders listed as my #13, the 125grn jacketed data for .38spcl+P shows Unique at 5.7-6.0grn, then turn a couple more pages back, the .38spcl data for the 125 shows Unique at 5.7grn DNR (Do Not Reduce). Scaling that up to your .357mag cases by adding 10% (multiply by 1.1), that's a 6.3grn DNR for Unique under the Speer 125grn TMJ.
Of note, however, Lyman #49 does show 4.0-5.7grn Unique under a 120grn Linotype LRN in .38spcl cases and 4.0-6.0 under a 125 Jacketed bullet in .38spcl cases, so scaling that load, that puts you down around 4.4grn Unique under a 125grn Berry's in a .357mag case.
So pick your poison - 6.3grn Unique under the 125grn Berry's in a .357mag case, 5.7grn Unique under the 125grn Berry's in a .38spcl case if you only use Speer plated data, or maybe as low as 4.4grn in the Mag case or 4.0grn in the Special case if you use Lyman's lead bullet data.
For two really low end powder puff loads of which I have ran THOUSANDS, I run 5.0grn HP-38 under Rainier plated 125's in a .357Mag case, and 4.0grn Bullseye under 93grn Meister LRN's in a .38spcl case. Shooting the Rainier 125's out of a .357mag Redhawk has almost no perceptible recoil, less than a 32H&R Single Six.