The first mash is boiled for 4 hours before mixing it with the first runnings of the second Mash to create the wort for the main boil.
Mash is BOILED?! I clicked on your link but it wouldn't let me view the recipe. Are you sure it said boiled? That doesn't sound like a mash to me. Decoction would have some boiling to it, but it sounds like you described boiling the whole mash.
Regardless, I have done a double mash, or reiterated mash, before. My mash tun isn't large enough for a big beer. As far as I recall, Beersmith didn't have a profile for it so I had to Macgyver it. My design tab had my total grain bill (which was split evenly between mashes). I entered my mash time as the total time between the two mashes. So Mash 1 was 60 minutes and the Mash 2 was 90 minutes. So my profile said mash time @ 150 minutes. When I swapped out the grain in the mash, I paused the timer. I always use the notes tab as a log for every time I brew a recipe and I try to keep detailed notes. So this is where I kept things in order.
My system is pretty consistent so I wasn't super concerned with numbers, even though this method wasn't going to be true to my normal process. Ultimately I missed my target OG by 5 points. I brewed an Imperial Stout but didn't separate my pale and dark malts---I'd be curious how effective this would be. This was my process:
Mash 1 @ x temp for 60 minutes, with a lower than usual water ratio. After 60 minutes, drain the mash (I batch sparge) into the boil kettle and set aside. Sparge Mash 1 and drain into another kettle. Use Mash 1's sparge runnings as the strike water for Mash 2.
Mash 2 @ y (or x) temp for 90 minutes. Drain Mash 2 into boil kettle with first runnings of Mash 1. Sparge Mash 2 and drain into boil kettle. Go.
Keep in mind, I took gravity readings for each running so I had an idea of where my OG would be in case I wanted to add sugar during the boil. I didn't have to in my case. But I did end up with more boil volume than I would have liked. I just made note of it so next time I can adjust the volume of water I'm using.
So ultimately, BS3 didn't have an option for this. So I had to manage it myself.