When I started making bows I was in Tasmania. I tried many times to make bows from tea-tree, though I never ever found one that would split straight - most of them would twist at least 90 degrees along six feet.
I tried what was known locally as Silver Wattle. It worked really well. Even a sapling just over an inch in diameter could make a nice bow of over 40 lb at ~28".
I made one from a young blackwood tree. It hadn't even fully transitioned from the classic acacia leaves to the older lozenge-shaped leaves. A sapling 2" wide decrowned and flattened on the belly. About 40 lb and shot reasonably well, though in retrospect was probably too green.
Horizontal apparently makes a brilliant bow. A number of years ago I managed to secure a small few half-rounds, about five inches across, long enough to make billets. I'm keen to make bows with them but owing to their rarity I fear a mistake. Horizontal has previously been used to make axe handles. I think woods that make good axe handles probably make good bows. Before I make bows from the billets I will do some scientific testing to find the mechanical properties and report back.
Three inches wide is pretty wide, but is also pretty safe. I reckon tillering a successful bow in the early stages is more important than making a bow ith superb performance. If that means making a bow wider than it should be with slightly less performance, then so be it. You'll still have something that shoots and you will still have learnt a great deal from the tillering process.