This is very personal! Different people like different methods, you may like this onw even though BEagle doesn't. I am a navigation instructor (ATPL groundschool) as well as a flight instructor, so can describe a dozen slight variations on pilot navigation.
I use the 1:60 rule myself (military technique, very flexible), but generally teach a method similar to the one you have been shown for my students, except on a leg less than about 20 minutes long I will rarely use more than 1 check feature. I always start by teaching the "double track error" method for regaining, as you have been taught. However with most students (at least those whose navigation teaching I start, rather than inherited students) I try to avoid even track splits, where the check is exactly half or a third of the way along, and instead choose indentifiable features at about half or 1/3 of the way along. For estimating angle off track by your method I suggest marking a line (in a different, pale colour so as not to obscure the chart) at 10 degrees off track on one side.