Omnisphericus I note you capitalized the "IF" there!! Clearly, a difference of house systems changes the situation - sometimes dramatically. Bernadette Brady for example advises using Alcabitius for determining the Hyleg and the Alcocoden - what would you advise?
I also use Alcabitius house division, and Regiomontanus as well.
But WH system is not wrong too.
Alcabitius house system was used by Bonatti as far as I know, and many medieval astrolgoers has used it.
Yes, Bernadette is strict and concrete in defining one system only and she does this in order not to confuse the students.
For example, for finding the Hyleg she is recommending the Bonatti's system only (in her courses), for dignity table she's using Egyptian terms instead of Ptolomy's and etc.
She must make choices and decisions. Because if different students use different techniques, they will all get different results.
Bonatti in his book has listed how different astrologers (like Abu'Ali, Ptolomy, Aomar and etc.) are allowing different places for the Hyleg placement. And out of this you can have different results.
For example, Ptolomy is not allowing the 8th house for the Sun's Hyleg, while Bonatti is accepting it if in masculine sign. Ptolomy is not allowing 9th house Moon because she is impeded, but Dorotheus accepts it if in feminine house and etc. Don't get me about the judgments of the astrologers (who was allowing what), maybe I'm wrong in listing the names but I just want to make a point.
So, using different house systems can also be a problem in making judgments.
Me for example, even though I use Alcabitius, if Sun is i 11th, but in the 12th sign, I note that and having it in to account in the final judgment defining the Hyleg.
And for the rule of which almost all astrologers of the medieval period agree, that is, that in order a planet or point to be Hyleg, one of his dignity rulers must be in aspect with it, I use WH aspects too. I see this Robert Zoller doing it. But if some other dignity ruler is making more concrete aspect (by degrees), that one for sure is stronger and should be taken into account before the WH aspect.
This is all a matter of improvisation of the experienced astrologer.