When I first read HoH:S, I thought that the debate rules presented in the Tytalus chapter could be used by anyone. But reading Ars and Academe, p.104, it appears this is not the case, and that Tytalus magi are the only ones who can debate! How do you play it?
I might be wrong, but I think you've turned it on it's head. A bit anyway.
Anyone can debate, using the system in A&A (Disputatio meaning... debate, right?)
Most academics are caught in this system - not because of rules but because of training - they are not used to whatever all out methods the tytali will use.
But characters without that rigidity of training can use the tytalian system, though possibly at a disadvantage.
Unfortunately when anyone tries to complain about this the Tytali point out the other magi aren't allowed to debate the matter. 
(Of course if the magi of House Tytalus debated whether they should allow other magi to debate half of them probably would be for it!)
What I'm still trying to understand is this. Take a ... Guernicus magus at Tribunal, one without academic training. Can he try to sway the Tribunal as a Tytalus would do? And if a Tytalus engages the Guernicus in debate, can the Guernicus use the full range of debate rules in HoH:S, or the more limited one in A&A, or ...?
The question is, have other Houses been exposed to House Tytalus's debate techniques sufficiently well enough to have absorbed them as part of their academic training in preparing apprentices. In short, no. However, if one can convince a Tytalus to teach these techniques...then all bets are off. But, on average, I think only a fraction of magi would know how to debate like a Tytalus. A couple of debates with different Tytalus magi might satisfy the learning curve... Or, the "closer" of House Guernicus who has matched wits with various debaters from House Tytalus in the past might know and teach Quaesitores these techniques.
In other words: YSMV. 
The problem is that, if you read the HoH:S rules on debate, it seems pretty clear that they are meant for everyone -- even non-magi defending their cases in mundane courts of justice (see p.92).
The author of Art & Academe seems to have missed this point, implying that the rules in HoH:S can be used by Tytalus magi alone; that a more limited version of the rules can be used only by trained academics (as well as Tytalus magi); and that everyone else just can't debate at all.
I would at least argue that magi are, in fact, trained academics. At least equivalent to Educated virtue, whether they have that or not. They may not be Magisters in Artibus, but they should at least be sufficiently capable to argue by the academic methods. As far as other people arguing, they do it all the time, and you might just do something much simpler for those arguments...
I think this is very much a...what do you want in your saga type of question. I haven't encountered this issue in any of my sagas I've been involved in... So... What problem are you trying to solve?
Basically, in my sagas I've seen a bunch of "political" characters, from magi trianomae to wily mundane merchants.
For them, debate is like combat for "warrior" characters. So I like to use debate rules when they are involved, because it places those characters in the limelight and allow fairer, less arbitrary resolution even when the players rethorical skills are not a match for those of their characters. Note that using debate mechanics does not detract from roleplaying -- you still have to roleplay a maneuver or you wan't be able to use it.
I used to play with the adapted rules from Dynasties & Demagogues that one can download from Atlas's website (the rules are here and the maneuver interaction table is here). Those are fantastic in terms of colour -- really a lot of fun. But with a bit of experience I have to say they are not terribly well-balanced mechanically, and are a bit daunting for newcomers. When HoH:S came out, I adopted the debate rules there. They are simpler than the D&D ones, and even though not as colourful, they are more well-balanced. I disliked the fact that A&A retroactively, and contradicting HoH:S, limits them to Tytalus characters alone, explaining that they are the product of the "finely honed" rethoric of that house.
I simply houseruled against this silly retcon. But I was wondering what the general feeling was on the issue. Obviously, this will seem a very marginal issue to anyone who simply roleplays all politicking, possibly with just one roll on an appropriate ability to gauge how things go (but then, any discussion about combat will seem very marginal to anyone who simply roleplays it, and makes a single ++stress roll for each contestant to gauge how things go).
Well, in a saga such as yours, I'd say that the secrets of the Tytalus techniques are out there and relatively easily acquired.
There is something to be said on both sides of the argument, but in a politics heavy saga, I'd be inclined to let these secrets be open to any who pursues them (and these could be magi of other Houses at gauntlet) but just give House Tytalus an arbitrary bonus of some sort. Tytali are well indoctrinated to these techniques having lived them for many years, during their apprenticeship. I like the idea of House Tyatlus being really good at arguing, and having techniques that no one else does, which could be underscored by them arbitrary bonus...
Actually, Tytalus magi do have some subtle advantage. First of all, they have the [strike]Strong-Willed[/strike] Self-Confident virtue, which is probably the best Virtue for this type of stuff. Second, while most magi tend to have decent Artes Liberales and Leadership, Tytalus magi tend to have high Intrigue and Guile as well (for their intrigues and impersonations). This gives them another advantage against the "average" magus using the debate rules, because they can adapt more readily to what their adversary does.
Self-Confident, not Strong-Willed, but point taken.