Decide whether you want to matte your image in 4:3 or 16:9 format. Then round up the width to the nearest factor of 3 for 4:3 or 9 for 16:9. Hint: If the digits of a number add up to a multiple of 3, the height is divisible by 3. If a multiple of 9, it's divisible by 9. Here I round 320 (digit sum is 5) up to 321 (digit sum is 6, divisible by 3). Then multiply by the desired aspect ratio, in this case 4/3. The math tells me that my desired width is 428.
In QuickTime, scale the matte (currently in memory) over your rotated video as follows: Select the entire video (Edit -> Select All, Command A) and then add the scaled matte (Edit -> Add to Selection & Scale, Command-Shift-Option-V). The matte will cover most or all of your video.
Select Video Track 2 and click Visual Settings in the movie properties window. Locate the layer control at the bottom of the settings. Adjust the layer to increase its setting from a negative number to a positive one until the hidden video pops out in front of the matte.
To center your image, you need to do some more math. Subtract the width of the rotated video (240 in this case) from the width of the matte (428) and divide that number by 2. This (94 in this case) is the offset you'll want to use.