OK, several things are sticking out. First, you have the batch sparge to divide the sparge into 'equal size batches'. So when the sparge is configured, it will make the sparge steps of equal volume.
The recipe you attached had two sparge steps following a draining of the mash tun. If I take off the 'equal batch sparge' selection, it changes the sparge volumes to 5.56 gal and 3.9 gal, with the limitation being the size of your mash tun with wet grains and your mash tun loss. If you change the sparge volume to fill 100% of the mash tun, you shift about a gallon of sparge water into the first sparge step.
Next, you are mashing at 1.25 qts/lb of water, which is about the minimum level you can effectively mash at and get good extraction. Try upping this ratio a bit to make better use of the volume of your mash tun. You have about 1.35 gal of free space in your mash tun and can transfer that to your initial infusion by increasing your water to grain ratio to 1.4 qts per gallon.
Since you are trying to fit a 12 gallon batch through a 10 gallon mash tun, this is probably about as good as your are going to get. My guess is that when you have a higher grain loading and slightly more sparge water, that it bumps up against the 90% capacity limitation for the sparge creating third water addition. Since you have it set for equal sparge additions, it takes the total sparge water and divides it evenly among the three sparge steps. This creates the sub-optimal (in terms of throughput) sparge volume additions that you describe.