I don't think the interpretation of daily text there is too bad - focusing on Paul's ministry as one example of something of his to imitate seems acceptable to me.
However, I do agree that quite often the org stretches the meaning and application of the daily verses it chooses, so as to try and make a link with their self-defined "faithful and discreet slave", to promote pioneering or Bethel service, or another of their own non-scriptural inventions.
One thing that interests me is that in the comments on that verse, they say the following (bold mine for emphasis):
Elders can imitate the apostle Paul not only by preaching from door to door but also by being ready and willing to give a witness on every occasion. (Eph. 6:14, 15) Like Paul, elders can use the time spent in the ministry to train others, including ministerial servants. (1 Pet. 5:1, 2) But elders should never be so busy caring for assignments that they have no time for the preaching work. (Matt. 28:19, 20) To remain balanced, they may on occasion need to say no to some assignments. After prayerful consideration, they may realize that they could not care for an assignment without neglecting the more important things, such as conducting family worship, having a full share in the preaching work, or training their children in that activity. They can be sure that Jehovah understands their desire to be balanced in all things.
It's interesting that they explicitly say elders may need to "on occasion" say no to assignments. They would never have said that in the past, I don't think, but sheer pressure on the brothers in recent years is making the org have to soften their official line despite there being a lack of new brothers coming forward, and I think that will have the effect of actually accelerating the shortage of men to take on assignments in future.
Although they don't give any detail on what "say no to some assignments" might mean - probably to try and cover themselves - that itself could backfire on them, as brothers will decide for themselves if they've had enough and what to turn down, and there's not a lot the CO or other elders can do about it apart from threaten to remove the elder's appointment, which would just make the situation worse.
Another case of the GB being stuck in a dilemma due to their past complacency and failings.