Bismillahi Al-Rahmani Al-Rahim
A Bit About Ibn Taymiyyah
Isa Martin wrote:
Dear My Respected Brother Musa,
   Assalaamualaykum wa rahmatullah.  It would be interesting to learn about the place of Ibn Taymiyah and Ibn al-Qayyim al-Jawziyyah within the Hanbali
madhab regarding their legal opinions.  [...]  It is also important for Hanbalis to know where the sources of acceptable rulings can be found.  You mentioned that Ibn Quddamah's Mughni is acceptable as a strong minority positions.  For instance, in Zad al-Mustaqni it says that all filth must be washed 7 times but in al-Mughni it cites 3 times (with the exception of dogs and pigs) as good enought.  Is this an example of two different strong opinions in the madhab?  Wassalaam.
 [end]

People have a very wide range of opinions when it comes to Ibn Taymiyyah and Ibn Qayyim Al-Jawziyyah (Allah have mercy with them both). We're all familiar with one extreme that considers them among the greatest mujtahdin and awliya and gives their positions precedence over all others, and with the other that considers them among the greatest innovators and riffraff that this umma has ever seen and considers everything they say superfluous or immediately rejected. It seems to me that these two Muslim scholars should be treated the same way we treat all other Muslim scholars: that they have opinions that are correct and others that are not.

Imams Al-Thahabi and Ibn Hajar have written fair biographies of Ibn Taymiyyah, and Muhammad Abu Zahrah has included a biography of Ibn Taymiyyah in his series on the great imams. These three authors mentioned things both for and against Ibn Taymiyyah, which is the approach endorsed by the muhaddithin. Every other work that I can think of sticks to mentioning just one side of the story, following one of the two extremes I mentioned, and tend to quote out of context. The recent Fatawa Ibn Taymiyyah Fi-l-Mizan is an excellent example of books that assume that everything Ibn Taymiyyah had to say was wrong; poor editing and poor scholarship to boot.

While Ibn Taymiyyah and Ibn Qayyim Al-Jawziyyah are both extremely well known, I'm not quite sure how much influence they really have had on the actual rulings of the mathab itself. I have found that some of the opinions attributed to them should actually be attributed to Ibn Taymiyyah's grandfather, Al-Majd, the author of Al-Muharrar. This is an area that should be studied, since in some cases it may give more legitimacy to some of odder opinions of these two imams; and I admit that some of those opinions would be quite useful to have. `Ali Mardiwi's Al-Insaf would be quite helpful in carrying out this research, since it gives a list of who held what position for most of the issues mentioned in books of fiqh.

I apologize for not being able to give a better answer, but I'm quite skeptical of much of what has already been done. Research is not supposed to be done  with the results pre-determined.

As for following opinions in the mathab, my sheikh says that any book that was used for fatwa can be followed for personal practice. This includes the works of Ibn Qudamma; but something to keep in mind is that Ibn Qudamma's  position in Al-Mughni (his later book) sometimes differs with Al-`Umda (an early book). Sheikh `Abd Al-Qadir Ibn Badran has a hashiya on Akhsar Al-Mukhtasarat, and in it he sometimes agrees with the position of Ibn Qudamma over the position of the later scholars.

The example you cited, of removing filth, is an example of two strong positions in the mathab. You could follow either one in your personal practice. Some scholars in the mathab hold that it is enough to simply remove the filth, regardless of the number of times; this is an opinion that my sheikh prefers, but he is quite clear in it being a personal preference and not being the mufta bihi in the mathab.