Short answer: They don't even try anymore...
This was the topic I started researching when I decided it was time to get off the fence re being a dub. I started by re-reading the appendix to chapter 14 in the Kingdom book, first printed in 1981. A careful reading will reveal that even the Society admits that all the weight of archeology points to 586/7 as the correct date. So they fall back on their misinterpretation of the scripture in Jeremiah about the 70 years and the old "we rely on the Bible over mans dates", evern though nothing in the Bible supports 607.
Well that book is over 20 years old. Surely if any new archeological evidence has been discovered since then that would support the 607 date, it would be a front-page Awake! article, at least. But there has been very little said on the topic, which leads me to suspect there has been no such find.
So then I took my questions to an elder, very smart guy, works for IBM, who claimed he had some secular evidence supporting 607. After calling his bluff, I finally pinned him down at the Hall, where he admitted he had no such evidence. As we are standing there after the meeting, people milling around, he very quietly concedes there is no real secular support. But he rationalized to himself that since this system cannot possibly continue much longer(in his mind, anyway), he needs to believe in the Society's promises.
So that was kinda the end of my 'research' phase...
No Apologies