that was the first time in more than 30 years of teaching th

it(this,that) be the first time that……这个结构中的that实际上是替代了when,它和when都可以省略.使用that是一种口语用法.
如
This is the first time (when/that)he had trouble with the boss.这是他第一次麻烦老板
一般情况下,during是必须有一个固定区间的,其后的时间段必须是确定的,而不是more than 30这种多于多少时间的表达.不过在实际运用中,往往不必严格规定,如during more than a decade on the PGA Tour,Tiger Woods has transformed the game.
The house where Amália Rodrigues lived during more than 40 years

这里in 我认为可以换作within,但不能换作During, during 强调1个过程中发生了什么，eg: During the course of his study, he leart much more knowledge. 此句话中的IN表示这一段时间，听到如此赞美是非常的不容易，而不是强调他得到了此赞美这一结果。（强调的意义不同）
至于that, 这里是It is .... ...

不行.in 是说在30年里.语法上也较通畅的. during 用法不一样,在这句子是不通的. during the last 30 years of teaching, he had never ......
后面的that是需要加的.

in 不能换成during,因为in后面有more than 30 years of... during 必须有一个相对固定的区间，如during his 30 years of teaching...
that 不可省，是that 的定语从句

我觉得in可以换成during，that也可以去掉

in 不能换成during，因为有more than
that 不可省,这是强调句，固定结构It is+呗强调部分+that(强调事物)/who(强调人)+其他