Irish oak doesn't grow where I live, but I've tried making a couple of bows from English oak (Quercus Robur) which, from what I've been able to gather online, is very similar in properties to Irish, used interchangeably. The heartwood of English oak seems to be very strong and elastic in tension, in my experience. Probably a great candidate for a sinew or bamboo backing. The sapwood seems to be week in tension in comparison. One self bow I made, with sapwood in the back and heartwood in the belly, broke in a spectacular fashion. Air humidity was up, so if anything the wood was a bit wetter than I would have wanted, and still it took almost no set whatsoever and the break was a textbook tension failure with no signs of compression damage anywhere. Another bow I made (lower weight) stayed in one piece with the help of a rawhide backing.
Again, I haven't tried Irish oak but assuming it's identical in properties to English, I'd say this. The bow you describe is a big one. It's at least 1 cm wider and about 8 cm longer than my go-to dimensions for elm for a bow of similar design, weight and draw. With a flat enough back, it should stay in one piece just fine with some careful tillering. It's a pretty dense wood so take care to keep those tips as light as possible for a smooth cast. With a rawhide backing, you'd probably be able to shorten the bow a 2-4" without any risk of breaking it, and I think you'd get a more smooth-shooting bow.
But then again, It is a different species so all this is basically guesswork...