Coming to the basic issue of why there are differences among various maThs, knowledge of what is meant by ekAdashi astrologically/astronomically is necessary.
As you would know, there is something called as 'zodiac'. It has got more to do with astronomy than with astrology. AFAI Understand, the vedAN^ga 'Jyotisha' deals with astronomy rather than astrology.
a. The positions of grahas are 'fixed' against the backdrop of 27 constellations. In this system of 'grahas' are included Moon, Sun and two points in space related to Moon's position that are considered Rahu and Ketu.
b. These positions are calculated with (i) the lattitude/longitude of the place and (ii) sun-rise time at that location. People used to having a Timezone over a large area might have some questions regarding point (ii), but suffice it to say that all deviations due to Time-zone concept get nullified.
c. For example, as of now i.e. at 3.09 PM in Bangalore, the Moon is at 22 degrees, 4 minutes (where the full zodiac circle measures to 360 degrees, just in case somebody doesn't know :-)) of Aries (Mesha), the Sun is at 0 d, 27 m of Sagittarius which is 240 d, 27 minutes from the 0th degree.
d. The tithi of the day is determined by the relative distance between Moon and Sun. If the distance between Moon and Sun is 180 d, it implies that earth is in between Moon and Sun, thus, you would have a full moon day. If the distance between Moon and Sun is 0d, the tithi is amAvAsya.
e. When the Moon has advanced the Sun (it will always lead the Sun because, relative to earth, moon completes its cycle faster than sun) by 12 d, it is considered one tithi.
f. ekAdashi is when the distance b/w Moon and Sun is in the range of 120-132 degrees (it is shukla ekAdashi) or in the range of 300-312 (it is krishna ekadashi).
g. All the rules of 'one should not fast on ekAdashi that is tainted by dashami' is 'executable' based on the above calculations. If at the time of sun-rise, the tithi was dashami tithi, but rest of the day was ekAdashi, then no fasting. These rules are laid down in Srimad Acharya's KrishnamrtamaharNava, but there are similar references in the purANAs that some texts such as dharmasindhu and nirNayasindhu also refer to.
Now to the actual problem:
The above theory remains same for all maThs. However, notice that the (radial) distance b/w the moon and sun can be calculated if only the position of 0th degree in space can be fixed accurately. That depends on something called as 'Ayanamsa'.
The method for calculating the ayanAmsa is subjective and has been explained differently from j~nAnis of different maThs. Uttaradi MaTh, AFAIK, follows Chalari Acharya's 'smrithyarthasAgara' or 'smR^iti muktAvaLi', while Sri Raghavendra Swami's MaTh follows the Krishnaavadhoota paNDita's work (I don't know its name). I am not sure what the aShThamaThas follow.
That these methods are from jnAnis and well-accepted people imposes the actual problem, ironically! It is rather that every person, scholar or otherwise, living now has accepted one's own limitedness in knowledge and thought and consider it dangerous to tread a path against the methodologies of one's superior; which is why many attempts to reconcile have failed.
Attempts that I know were one from Sri Satyadhyana tirtha and MANY from Sri Vidyamanya tirtha. Perhaps there were other attempts, but I don't know. Such attempts have failed because people who know astronomy were afraid of going against their superiors. Note that these superiors were not just chronologically superior, but actually so in knowledge.
It is not that this issue cannot be solved, but it needs heavy leadership
skills and real courage, backed up by solid intellect. But right now, our
tradition has so many other things to focus on (Read the concluding part
of "History of Dvaita school of Vedanta"), that this issue is at the backseat.
One might object to relegating this issue quoting Ekadashi's importance
etc. But given that we don't have what is needed to solve the problem,
we should find solace in the fact that the Lord accepts many activities
directed by gurus, though it might seem adharmic.
To raise noise about this issue and how it represents the banal attitude of mAdhvas etc are all timepass activities one does when one does not know what to do. There are many controversial issues on earth and mAdhva tradition has a good share of it. To indulge in discussions on such or to expect answers to such, I doubt, will bring in anything that will aid you in following Srimad Acharya's dictum:
smartavyaM satataM viShNuM, vismartavyaM na kadAchit(?)
Whatever activities one does, one should always think of Vishnu and should never forget Him in their activities.
Until we get there, I don't think laymen like us should get into these controversial issues.