A possible objection that a JW might come up with is that a time is 360 days while a year is 365.25 days. I was under that impression when I was a Witness. Actually a time just stands for a period of time. It could be a year, a month, a day or some other time period. I can't see any indication that the times mentioned would even have to be years. It would make a lot more sense if Nebuchadnezer was insane for seven days or seven months instead of seven years. Otherwise, it seems pretty strange that he could be gone from his throne for that long without it being mentioned in historical records or without his Kingdom being taken over by someone else.
If you accept that it was actually years, it would only make sense that the kind of year be consistent. You could use years of 360 days for both if you allow for extra leap months. Since seven periods of 360 days differs from seven solar years by more than a month. You would have to add one or two extra months for either 2,550 or 2,580 days. 3 and a 1/2 times might equal 1,260 days, but it could also equal 1,290 days if there is a leap month, a time period that is also mentioned in the Bible. 7 times, however, would have to have at least one leap month.
There is a precedent for the Bible to mention the number of days in a period of times when it is important, since you wouldn't know otherwise. Since the Bible doesn't mention the number of days in the seven times, it is reasonable to conclude that it doesn't matter.
I would love to try to get a JW to explain why two different types of years are used in the same prophecy. I think this could be more effective than concentrating on the 607 verses 587 debate.