How about trying EdWort's Apfelwein scaled down to fit in your set up? Follow the directions below changing them for your Mr. Beer.
If it is 2 1/2 gallons the the recipe would be:
2 1/2 Gallons of Tree Top Apple Juice from Costco
1 pounds of Dextros (corn Sugar)
1 packet Dry Montrachet Wine yeast
1. Sanitize your carboy (I love my Better bottles) and big funnel.
2. Pour half of one gallon of juice in the Carboy. Then add 1 pound of Dextrose to the half empty bottle of juice. Put the cap on and shake it up to dissolve the sugar.
3. Repeat step 2 with another gallon of apple juice and the other pound of Dextrose
4. Pour the half bottles of juice/dextros into carboy
5. Pour the rest of the juice into the carboy saving about a quart
6. Sprinkle the yeast into the funnel then rinse with the rest of the juice so all the yeast is now in the carboy.
You can fit all the juice in it, don't worry.
Wait 4 weeks at least then keg, chill, & carbonate. I don't do a secondary, but you can if you want to age it beyond 4 weeks. I would not rack till it clears like the first bottle.