In the Schmitz process, the malt is doughed in and rested at 122F to reduce viscosity. If beta glucanase hasn't been kilned out of the malt it will reduce beta glucan and produce glucose. If it has been kilned out, proteolytic enzymes that survive kilning will reduce beta glucan. Then, the mash temp is raised to 150F, starch gelatinizes at 149F. At 150F beta is active, along with alpha. After gelatinization, both enzymes will be active in reducing large a and b limit dextrins, in somewhat of a balance. After resting at 150F the mash liquid is run off and the main mash is boiled, causing hard starch to burst and go into solution. The main mash is cooled to alpha temps. The enzyme laden liquid is added back into the cooled, starch laden mash and rested until conversion.
In the method you are proposing. The mash is doughed in and rested at 145F, mid beta temp. Beta is slowly working on the starch chain that alpha is slowly breaking down into shorter chains with a reducing end and a non reducing end. Beta is slowly chopping off two glucose molecules from the non reducing end of the starch chain, mixing with one molecule of water, producing maltose. After resting 15 minutes at 145F, the mash liquid is ran off. The main mash begins to gelatinize at 149F as it is brought up to a boil, at 169F hard starch bursts and goes into solution. Then, the mash is cooled to 160F and the enzyme laden mash liquid is added back. Here's a small problem. Beta is denatured, the production of small b-limit dextrin is reduced. Iodine test will show excessive a-limit dextrin by the color of the iodine. Imbalanced product. A rest in the beta range during gelatinization should be perfomed, before removing the mash liquid. The 122F rest called out in the Schmitz method is deleted in the proposed method. Maybe, not a good idea? Even though the malt being used is probably high modified, a time and temperature controlled rest is valuable.
One of the things that a decoction does, is it forms a cleaner wort. Part of the reason for a cleaner wort is due to the way the filter bed settles. When mash is boiled, air that is entrapped in the husk is boiled away. With air boiled out, the mash settles a little more evenly and is denser than in an infusion. The infusion floats a little. By squeezing the last ounce of liquid from a grain bed that is used for filtering and is loaded with mud and protein goop eliminates a couple of benefits of the decoction method. In the proposed method, the mash is contained in a basket and brought to a boil. The basket will be some what of a heat sink, it might take a little more time to bring the mash to boiling.
I don't see anything wrong with using the process with the present equipment. Experimentation creates a learning curve. If it fails or works something is learned. However, for the first time, it might be best to follow the directions given by the guy that invented the process. The small grain bill needed to produce three gallons of beer is small. It wouldn't take a large vessel to hold a couple of qts of mash for a decoction. Then, you could dough in cooler, allowing pH to stabilize and to utilize certain enzymes that might not have been kilned out, before pulling a decoction. Something to consider; depending on the decoction method used, low modified, low kilned malt is a good choice. When reading about the decoction method, authors mention various temperatures to rest the malt at to utilize certain enzymes. The problem being is that enzymes like beta glucanase, maltase, dextrinase, phytase are generally kilned out of modern malt. Proteinase is tougher to kiln out and survives up into mid beta temps. The Kolbach or the SNR number of the malt is used to determine the length and temp the rest should be when employing a protein rest. Crisp Malting is producing Crisp Euro Pils. It is produced for use in the programmed mash method or decoction method. I have used the malt and phytase isn't evident. Weyermann light Boh Pils and dark pils floor malt are other good malts for using in decoction recipes. Sometimes, looking at what is on a malt data sheet isn't a bad idea. There are certain numbers on it that can help a brewer to decide what process will work the best with the malt.
Because of family life, kids, jobs, etc., finding time to do tri-decoctions is tough. I don't blame a brewer for trying to shorten the process. After all, George Fix invented the programmed method to mimic a tri-decoction.
Good luck and BREW ON!!