I have a 3 gallon cooler, so that is why the sparge volume is actually more than the 2 gallon mentioned in the article. I haven't actually done a batch yet, I have still just been playing around with numbers in Beersmith trying to get the numbers figured out to make sure I can follow the process.
I actually have a 5 gallon cooler as well, but only have a 5 gallon brew kettle. So, basically I am still doing a partial boil with extracts up to now. I plan to just do partial mash partial boil for now. Based on other posts here it seems like it will probably be better to use the smaller cooler to avoid heat loss during the mash.
Makes sense. FWIW using a 5 gallon cooler would probably be fine, but you might as well use the 3 gallon cooler for now.
Sorry to stray away from the original topic, but as someone who's spent a lot of time tweaking this process, let me suggest a few things:
1) Mash as much as you can. The BYO article mentions a 4 pound mash, but I found I could easily do over 5 with my 2 gallon cooler. Since you have a 3-gallon cooler, you should be able to push that upwards of 7 or 8lbs without much trouble.
The grainbill you're playing around with right now in your calculations is at 3.75lbs. You could easily double that and have no problems mashing it.
2) Batch sparge in your kettle. I found that transferring the first runnings to the kettle, having a third vessel to heat sparge water, etc., was totally unnecessary. Mashing in the cooler, transferring the grain to the kettle where containing heated sparge water, and then transferring the first runnings into the kettle makes way more sense and is much easier.
3) Get Fermcap and boil as much as you can. I used to struggle to boil more than 3 gallons or so without boil-over issues, and then I started using Fermcap. Now I can get a nice rolling boil going at 4 gallons with no boil over risk.
For starters I'd consider mashing ~7 or so pounds of grain with 9qts of water, and then sparging with 9qts of water. With grain absorption that should leave you around a 4-gal boil volume. That should be about right, I think. Mashing and boiling as much as you can is kind of a no-brainer as you're increasing the quality of your beer and making it less expensive for basically nothing.
Just some ideas I wish I'd come up with a year ago