That is spot on April. I mean, sure a juice is best drunk immediately after being made, but the reslity of that is impractical while fasting. You really do need to plan ahead. The key is storing the juice really well. To do this you must fill up your containers right to the top. If you don;t have quite enough juice to do that, top it up with a bit of water. Also, use single serve size containers, because if you poor some out and leave some in, then the remaining juice is going to oxidate quite quickly (due to contact with air). By having them filled to the very top of the container you slow down oxidation.
I usually make 2 days worth of juice in advance. This also helps with limited space in the fridge.
And yes, definitely, if you can start on a weekend, that would be best. In fact, if I were you, I'd start Friday evening so as to try and get through the worst of the detox before being back at work on Monday morning. Also, consider both starting on different days, so one of you can pick up the slack while the other is feeling worse for wear.
You made me laugh about your first few days April. I nearly cried on day 1 hahaha. This is the blog post I wrote for the first week of my first fast: http://planetsarah.com/2012/05/16/reviewing-week-1/
You might find this page helpful: http://thejuiceplanet.com/storing-and-transporting-fresh-juice.html