The last four years I have been teaching Greek more and more via the Living Language method. The first year, I used Hale's stories from "Let's Study Greek" along with my own curriculum that I have been developing. I was unaware of Dobson's new edition (which includes the accents) at that time. Three years ago, I considered Dobson, but did not use it; instead, I kept developing pericopes from the gospels along with embellished stories relating to them. Two years ago, I started making my classes perhaps 50%+ immersive content. I considered using Dobson as my written text from the first day of that school year, and regret not doing so for that year. The reason is, that new learners need the written side-by-side with the aural. I did not start using Dobson until the 2nd half of the year; I lost a good part of my class about 10 weeks in, partly because they were not serious enough ( I teach in a non-academic environment), partly, because I was unfocused and did not have a clear-cut curriculum which progressed from easy to hard, limited vocabulary and forms, partly because I did not have a written text which explained some of the finer points of grammar.
I found that the progression of grammar points in Dobson matches much more closely to the vocab, grammar structures, and content that one uses in a living language environment. There are a few items which need to be moved up earlier; little needs to be deferred for later. The strength of Dobson is his constant diglott of Greek-English phrases and short sentences, where he constantly switches person and number. The problem with using only Dobson, is that the stories and elaborations get boring, and don't bring the student into the mix nor let their imagination run wild - a distraction which takes the learner's mind off the grammar and onto the content - and actually lets them acquire the language rather than memorize and rework grammar forms.
Objections that the book does not teach grammar fall away, once one realizes Dobson's goal is to get the student to learn to read ancient Greek, and not parse or analyze grammatical structures against the background of a Grammar-Translation environment. In my own opinion, grammar is best taught after the target language has been acquired or understood at a rate of 100+ words per minute. We don't teach grammar to English speakers until (1) they are old enough to have abstract reasoning (age 13+) and (2) have an excellent grasp of using their native language. We don't ever teach grammar to 1st or 2nd graders, other than to tell them, "We don't say they eats, we say 'they eat.'" At those early stages, we model correct use of the language where appropriate.
(1) my own limits in fluency with the language that still need to be built up. I'm aggressively working on it but I still don't feel ready
Well we are all in that boat. The main thing is to stay ahead of your students. If you have had enough years of Greek under your belt to be mentally aware of your aural/oral deficiencies, you can be assured that you will eventually get it correct. Students are forgiving and often oblivious of those minute errors that creep in; not being a native speaker, errors will always bubble to the surface. You will never feel totally ready to teach via a Living Language Method, but you can reinforce your skills by listening to audio, reinforcing patterns you teach by listening to those phrases used in a greater context. I've found that songs also help - they are a great source when you need to 'reach for a specific structure.' I started using 10% LL, and this year was up to about 80%. The more one teaches using LL, the more one realizes that students need the immersion experience, and not a half&half approach. I remember reading in the teacher's manual for Rouse's Direct Method (perhaps in Praeceptor), that students that were kept in this dual language method of learning were not as successful as those whose classes were 90%+ in the target language.