Tropical Zodiac: this is a complicated issue, especially since the constellations and tropical signs were roughly aligned during the first and second centuries C.E., a period of time that gave much astrology to the world.  The pictorial dimensions of the twelve signs of the zodiac stem from utilizing the constellations, not tropical signs, for astrological purposes (although there is evidence for the Hellenistic use of sidereal positions). But if we confine ourselves to the tropical zodiac, essential issues like symmetries of rising times and times above the horizon, which correspond to symmetries to the Aries/Libra and Cancer/Capricorn axes respectively, and the use of ascensions for predictive purposes will not be compromised.
Whole Sign Houses: these may be familiar through Vedic astrology.  According to this house system, the first house or place was the entire sign of the Ascendant and the eleven others proceeded around the zodiac.  This was the first one used and, in my view, has a compelling and enduring intellectual attraction.  Astrology’s subsequent use of quadrant system for houses is an accident of history and not necessarily a positive development in the field of astrology.  Although many people are habituated to quadrant house systems, it is worth practicing casting charts in a whole sign system. I suspect that you may find yourself continuing to use whole sign houses after you have tried it out.
Whole Sign Aspects: The Hellenistic tradition does not use aspect orbs as do modern astrologers, nor are there planetary orbs as used by medieval astrologers.  Using sign-to-sign aspects unconditioned by orb does not create an unwieldy amount of information. Instead, there is a strong limiting factor: the aspects that are most critical are from a benefic or malefic to a significator for a particular issue.  One does not use all aspects from each to each planet, nor do we find complex aspect configurations as we do in modern astrology.
Planetary-based Predictive systems: Modern astrologers are accustomed to using predictions based on transits – mostly transiting outer planets when they form aspects to fast-moving natal positions like the angles and the luminaries.  Ancient astrologers also used transits but did not emphasize them.  Instead, profections by year and by month can give detail to prediction for shorter amounts of time.  What is unusual to the modern student of astrology, however, is the prevalence of planetary lords or chronocrators to depict shorter or longer periods of time in a person’s life.  The interpretation of this time is based on the intrinsic natures of the planets involved and how they are placed in the natal chart.
There are chart factors from the Hellenistic tradition that are less demanding to the modern student and add to natal astrology.  These are considerations of planetary sect, orientality and other configurations with the Sun, lots and fixed star positions, triplicity lords and compound dispositors.  Having made the adjustments outlined above, a student of Hellenistic astrology may find these considerations of lasting importance in their understanding and use of astrology.