You can get a good amount of conversion just from steeping. A lot of the extract brew kits use unmilled grain, which is good for shelf life but bad for conversion (but still adds flavor), which is probably where you got the impression that steeping doesn't work. I think the primary reason for needing a mash tun is to handle the volume of grain needed for 5+ gallons of brew. If you are brewing less than that, you can get away with steeping in the brew pot, and equipment permitting, sparge using a colander or grain bag. Just add a little extra grain to account for conversion losses.

From my experience, you only loose a few degrees of temp over the hour of steeping in the boil kettle. I usually put a towel or two on top of the lid to help retain heat, and if needed, will pour some hot water in from the tea kettle to keep the temp up, but that is rarely needed.

For a quick, hipstery, overview of the gallon batch method go here, I use this method for my gallon brews, and the results have been really good: http://brooklynbrewshop.com/instructions

I haven't tried this, but here is the brew-in-a-bag method: http://www.northernbrewer.com/shop/brewing/biab-brew-in-a-ba...

I have a buddy in a similar situation as yours (kids, no time to brew). He has a killer setup (15 gallon, all-grain), and his solution was to just cut back to brewing a few times a year, and invite some buddies over to help. I think one gallon brews are best left to people in small apartments or for experimentation. In your situation, I would keep in mind the yield-per-time metric. A 15 gallon brew might take a few hours longer than a gallon brew, but it yields 15x more beers. Gallon brews are a good way to keep your brewing instincts sharp, but it won't keep your fridge full.