In your initial infusion at 62C, you will solubilize the enzymes you need to reduce the starches to sugars. At that temperature, however, not all the starches will be available, as the gelatinization temperatures for some of the longer and higher branched starches will not become soluble until you reach around 64C. When you drain the wort from this first infusion, you will carry away most of the enzymes you need for further conversion of the starches still in the barley kernels. Doing this will not perform what the initial intent of the mash profile you wish to occur -- the further reduction of longer starch chains into more fermentable species.
I see a couple of options for you. The first is to do as Bob357 recommends and move to a single infusion at around 64C or 65C. 64C should give you a slightly more fermentable wort.
The other is to use a decoction to raise the temperature. In the decoction, you will remove the thick part of the mash (grains and a little wort) and leave behind much of the liquid with the enzymes continuing to work on the soluble starches in the wort. Since you are really only looking to raise the temperature, you do not have to boil the thick decoction for very long, maybe a few minutes before returning it to the mash tun to raise the temperature. BeerSmith does give the amounts of grain/wort which needs to be removed and decocted to bring the temperature up to the next step. Through my own experience with this, I usually pull about 15% more for the decoction than it calls for in order to hit the target temperatures. My guess is that because I have done this with a BIAB mash and have the 'adjust equip for temp' turned off, that this is the main reason for needing more mass for the temperature rise.
Another concern that I have is the water to grain ratio in your mash tun from the start. I don't know how much grain is in your recipe, but if your initial infusion is below 2.6 l/kg then you will not have enough water to perform efficient starch solubilization. If this is the case, I would suggest another alternative which would be to split your grain bill in half and conduct two mashes back to back.
