Any take on this...how to replicate a step mash regimen with a single temperature infusion mash?

It is not possible to replicate a step mash with a single-infusion mash, but one can substitute a single-infusion mash for a step mash.

With that said, I have performed step mashes using an initial hot water infusion followed by boiling water infusions. I can derive and perform the calculations necessary to step mash with hot and boiling water infusions by hand because I understand an underlying thermodynamics concept known as specific heat capacity. For those with rusty math and/or physics skills, Brew Smith should be able to perform the calculations for you.

If one knows how much hot liquor one wants to use for the step infusion, then the calculation shown immediately below will compute the minimum hot liquor temperature for the infusion.

current_mash_specific_heat_in_gallons = mash_liquor_volume_in_gallons + (grist_weight_in_lbs * 0.05)

Note: a pound of grain has the same specific heat capacity as 1/20th of a gallon of water

step_liquor_temperature = ((desired_step_rest_temperature * (current_mash_specific_heat_in_gallons + step_liquor_volume_in_gallons)) - (current_mash_specific_heat_in_gallons * mash_temperature)) / step_liquor_volume_in_gallons

While the calculation shown above is useful, brewers usually perform step infusions using boiling water; therefore, what we really need to calculate is the minimum amount of 212F hot liquor that we need to raise the combined temperature to the desired step rest temperature.

Rewriting the equation shown above to solve for step_liquor_volume_in_gallons when using 212F liquor yields:

current_mash_specific_heat_in_gallons = mash_liquor_volume_in_gallons + (grist_weight_in_lbs * 0.05)

step_liquor_volume_in_gallons = ((step_rest_temperature * current_mash_specific_heat_in_gallons) - (current_mash_temperature * current_mash_specific_heat_in_gallons)) / (212 - step_rest_temperature)

Example

We mashed-in with 10lbs of grain and a hot liquor to grist ratio of 1.25 quarts per pound, which resulted in a rest temperature of 151F. We now want to raise the temperature to 168F using a boiling water infusion.

current_mash_specific_heat_in_gallons = 10 * 1.25 / 4 + (10 * 0.05) = 3.625

step_liquor_volume_in_gallons = ((168 * 3.625) - (151 * 3.625)) / (212 - 168)

= (609 - 547.375) / 44

= 61.625 / 44

= 1.4 gallons of 212F liquor

Now, let's verify that that value works with the first equation.

step_liquor_temperature = ((168 * (3.625 + 1.4)) - (3.625 * 151)) / 1.4

= ((168 * 5.025) - (3.625 * 151)) / 1.4

= (844.2 - 547.375) / 1.4

= 296.825 / 1.4

= 212F

With the above example complete, the computed hot liquor volume is the smallest volume of 212F hot liquor that one should use. In practice, one should boil at least this amount of liquor because the tun also has to be brought up the the desired rest temperature, which will require a small amount of 212F hot liquor above and beyond the computed value.

One last thing, if one is going to perform more than one step, one must start with a thicker mash because each infusion increases the amount of hot liquor that is necessary to raise the mash to the next temperature.

Note 2: Extra parentheses were added to ensure that people understand the order of operations.