I've done something similar to this for the past several years on every league set that I've bowled. I record every frame on a sheet of paper, giving the result of the frame, and I put the pins left above the frame. If I felt like I threw a good shot and was ripped off, I'll record a "pk" above the pin left (for pocket). At the end of the set, I have a complete record of every frame that I threw during the set, and the resulting pins left on every ball.
I take a blank sheet of typing paper and fold it into 1/8ths.....and on each 1/8th of the sheet, I can put 3 sets of games on that section. By the time I have one side of the whole sheet filled out, I'm looking at 24 sets (72 games)....then I flip the sheet over and start again on the other side. The data gives me a good chance to review exactly how well or poorly I performed on a given night, and it also allows me to track trends on a given lane independently. I even go so far as to circle the lane that I'm starting out on for the first game, so that I can track that lane across all 3 games. It makes it easier to see if an adjustment is in order, or whether I need to stay where I'm at. Once the automatic scoring system is reset at the end of the game, all of your info is gone, unless you are keeping a frame by frame account on the paper. You can see exactly how many 10-pins you left, how many 10-pins you missed sparing, and on and on.
I have to admit that sometimes the data gives you more truth than you really want to look at, but at least you have an idea of exactly how the night went for you. And, you know exactly how many strikes you carried during the set as well. I can tell you that it normally takes about 17 to 18 strikes to break the 600 barrier, although I have seen some sets hit 600 with 14, or other times open frames may increase the needed number to 20, but the 17-18 number is pretty average.
Anyway, it takes a few seconds worth of effort after every frame to record the info, but it also gives you something repetitious to do while you are bowling, so it becomes part of your bowling routine. At the end of the third game, there is no guesswork on how you arrived at your series number for the night.