Dig around on these forums for information about kayak/Oasis sailing and modifications/tweaks to rigs, etc - there is a whole lot of info there from a number of well-experienced exponents of the art.
FWIW my personal preference is not to bother with outriggers of any sort (I have an AI which I hardly ever use as such - I just use the AI hull and small sail with an adapter I made). I prefer my sailboats to lean and find that the sailing experience of a trimaran really lacks something. Of course this does increase the risk of a capsize but if you use common sense and sail conservatively this should not be a frequent occurrence (fortunately where I live we are frequently blessed with more or less ideal kayak sailing conditions - this may not be so true for you and others and your 'need' for more stability could be greater as a consequence of this and other personal/environmental factors) and as long as you are able to get back on board you the occasional capsize should be more of a learning than a life-threatening experience
You have, in the Oasis, a boat with the potential to make a really fantastic sailboat but this will require a modification. With 2 crew and just the one sail the Oasis sailing experience is boringly pedestrian - and the bendiness of the mast combined with the extra ballast of two people does not make the option of 'just going out in stronger winds to improve the experience' viable because the mast just bends off and the sail loses most of its shape and drive. Also, to solo the Oasis under sail, you really need to be in the rear cockpit (to be able to control the sail) but then to keep the bow down you will need to add ballast in the forward cockpit which, once again, has the effect of slowing the boat down and/or loading up the sail too much with the same undesirable effect on sail shape and performance.
But if you add a second sail at the bow the sailing performance is transformed - suddenly the boat has the right 'sail area to ballast' ratio and she sparkles. Plus, with a bit of thought as to sheeting/cleating arrangements and roller reefing, you can control both sails from the rear cockpit - and the boat responds superbly to trimming and is very engaging to sail. The front-seat occupant can participate too in a variety of ways such as weight trimming, controlling the foresail and raising/lowering the fins to help tacking and gybing.
I have not made these mods to my own (new) Oasis yet but I will do so soon and I can't wait - I tried my friend's Oasis schooner equipped with two sails and with both of us on board and controlling the sails jointly or from the rear cockpit only it was brilliant!
The other thing I am thinking of experimenting with is the addition of a full set of mast stays to reduce the tendency of the masts to bend and thus preserve sail shape and performance (though this, in my plans, will probably be at the expense of losing any roller reefing/furling capability) and with a forestay you have the ability to also set a jib (as long as the forestay is counterbalanced by a backstay, of course).... and, having flown a jib on my Adventure for a long time, I can vouch for the fact that at this point you are getting into seriously challenging and exciting kayak sailing territory
Of course as well as lacking the forward mast base, the Oasis also lacks daggerboard(s) - COME ON HOBIE: MAKE 2 MAST BASES AND DAGGERBOARDS STANDARD ON THE OASIS! - so, unless you also add some of your own, your upwind performance is going to be restricted due to higher than desirable leeway - but even with these limitations and the necessity of making some fairly serious mods to your boat I reckon that the result will be well worthwhile and will, in my opinion and experience, result in a sailing vessel with far more about it than any of the single seat/single sail Hobie kayaks, an Oasis trimaran and/or an AI (I haven't tried a TI so will give the TI the benefit of the doubt for now
...of course what works for me doesn't necessarily apply to others: it all comes down to things like personal preference, personal risk profile, sailing conditions experienced, intended use, need for speed, etc, etc. That said, I reckon you should give these ideas some serious consideration as you clearly want to sail your boat.