I have had some lift in the area you describe, as suggested ,, you may not need to put sinew there if it is static , also if it is working a bit,, a small sinew wrap in that area, or string wrap until it is cured would prevent that,, if it is working,, maybe leave a small sinew wrap in that spot,,
ok about the comments about oil,, of course you can bend with oil and then sinew back,, you have to clean the back of osage oil anyway, if you use lye or strong dish washer soap and boiling water,, the back can be clean of any oil you used and suitable for sinew backing,, I have made alot of sinew bows, that were bent with oil,, and the sinew has stayed on as long as 20 years,,,
just recently I had some sinew lift at the working recurve,,,it broke there as well when I first started to tiller,, so I did remove the sinew and start over,, i took a knife and carved off the sinew backing and then sanded,, I did not wash the back any more,, it has stayed on fine this time,, I think my problem was more glue related,,