Your home does not have to qualify for the home office deduction for it to qualify as your principal place of business. So you don't have to have one room exclusively used for business in order to deduct your business miles. From an examination point of view, however, I can see that the IRS could be more willing to accept your home as the principal place of business if you did. As I explained before, the whole tax treatment depends on your individual facts and circumstances. See this discussion.
As far as your record-keeping is concerned, the method you are using seems reasonable, because you are keeping a contemporaneous record of where you drove and when, and the business purpose. Calculating the mileage based on this information would be accurate.
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