I mash in a 10 Gallon Gott cooler - in a setup probably fairly similar to what you've got - and I think I'd either infuse with boiling water in the cooler, do a decoction mash to hit my temps, try a combination of those two techniques or, most likely, stick with my SOP and single-infusion mash.
Can you make a better beer with a multi-step mash? Maybe. I'm not sure that I could. I don't have any practice with that technique. I wouldn't try what you're proposing because I'd likely never use this technique and would, therefore, never get good-enough at this technique to make better beer than I could with my standard technique. My new mantra is, "Don't fight your system".
I say all of this with the caveat that recently (about a year ago) I decided to branch out and try a ton of new techniques. I think what I found, after 40-some-odd batches of experiments, was that all of these techniques can make amazing beer; however, none of these techniques are the secret to making amazing beer. The secret to making amazing beer, I feel, is perfecting a process that works well for your system. That's my current brewing philosophy FWIW.