In terms of the gradebook, your idea is fine. Though, it does not need to have extra points that you add in to get back to zero, if you simply set the assignment value to zero from the beginning. A zero point assignment can be graded as 10 points and it will add 10 out of zero to the total. If the extra-credit is participation, then this is easy: every student gets the same 10 points and so set default grade works fine.
It sounds a bit as if you want to use set default grades to add 10 points to each auto-calculated score, and that will definitely not happen. Either you will only enter 10 points into scores that have no grade, or your will replace the existing grade with 10, depending on whether or not you check the box.
The problem will be with the auto-grading. Quizzes do not have a true extra credit option. The auto-graded quiz worth zero points, will auto-grade as worth zero points. This is true in both classic and new quizzes. In classic quizzes you would set each question to be worth zero points, and in new quizzes you could set the assignment to be worth zero points, and then within the quiz have any point distribution you want. The grade shown in the gradebook will be a zero no matter how the students do. In classic quizzes that would completely defeat the purpose. In New Quizzes, the quiz will have auto-graded as a zero in grades, but the teacher can manually click through each submission in speed grader, see the auto-calculated total that is based on totaling the points from each question (before grades converts it to a zero), and update fudge points equal to the student's auto-calculated total. In grades, the fudge points will be seen as extra credit added onto the zero earned score. Once the teacher adds those fudge points it will display correctly. However, there is no indication in grades or speedgrader as to which student's new quiz needs to be graded (even if the questions are not autograded). To be managable, the extra-credit quiz will need to have an until date for the absolute last submission, and the grading will need to happen after that until date. The assignment should be set to manual grade posting, so that students do not get confused by the temporary zeros while they wait for the assignment to lock and the teacher to enter fudge points and post grades. (Oddly they will still be able to see the auto-calculated score on another screen, so they will know how they did instantly. On the same screen, they will later see the doubled score with the fudge points added even though the gradebook will only show the accurate total.)
Alternatively, the extra credit (new) quizzes can be set to "do not count towards grade" in the assignment settings with their actual value. Then, you can make a matching zero point assignment set to no submissions, and the teacher can manually copy all 280 auto-graded scores from the not-counted-but-graded new quiz to the zero-point-no-submission assignment. The grading will work as expected, after the manual copying, but the gradebook will be cluttered. The classic quizzes version of this would be practice quizzes, and copying the score to a zero point assignment would be tedious.
The most direct way to get this type of extra credit entered entirely automatically, is to set up weighted grades in two groups, one at 100% for all of the normal point based assignments, and one at whatever percent the maximum available extra credit will be. Then the teacher can add normal quizzes to the extra credit group, and they will auto-grade and enter correctly as a bonus above the total points in the 100% group. For the most accurate display of totals for students, however, you would want to break this down to a percent (and an assignment group) for each individual extra credit quiz. (Otherwise students will seem to earn all possible extra credit if they earn 100% on the first quiz.) The 100% group can be used for normal point based grading without any other adjustments by the teacher. (If they later decide to subdivide the points from the 100% group into weighted groups, note that the extra credit groups will not calculate correctly until there is at least one score in every assignment group that contributes to that 100%)
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