Dead space in the mash tun (recoverable or not) really only affects the calculation of the initial strike water volume and temperature. After that, the program really does not have this volume included. Additionally, the calculation of sparge water is basically a variable for the program to balance the water demand in the process in order to balance out all the water inputs which are user fed to the system. As the brewer, it is up to me to look at the values which are spit out by the program and either adjust or rationalize them for my process by manipulating the values I have input or managing my process to make the system work.
So, if I were in your shoes with your process, I would look at two different options. The first would be to adjust the water to grain ratio to provide for a greater requirement for sparge water. The second, and probably the one that I would be more likely to employ is to drain the mash tun down to attain a known amount of first runnings in the boil kettle and then adding the sparge water. Since the image you posted is too low res to see clearly on my computer I am making up numbers for the example below.
For example, if I had a strike water value of 8 gallons (3 being dead space) and I had 1 gallon to grain absorption, I would drain the mash tun to get approximately 4 gallons of wort in the boil kettle and then add in the sparge volume.