My suggestion is to forget the sinew especially for now.
Doing,a sinew backing is,messy, time consuming, and ment for short bows. So for a fledgling bowyer sinew is too much too soon. Sinew adds strong tension and would be too much for a lot of woods.works well with Osage and Hickory.
I had the same questions on backing,when starting out.
I've,settled on using bamboo and sometimes hickory as backing. Gluing in R/D.
On your white oak board if there are run outs in the grain that could splinter then a,simple backing like paper or cloth may help.
Go through with making the bow. Tillering etc.
Many first bows are best thought of as learning tools. Most don't make it long. Then add the backing before doing finish work.