NO! Don't make simple straight side grooves!
Your problem is the overlay is narrower than the belly of the bow so as the string swings upwards along the belly it is rubbing.
Your two pics show all you need to know! You've seen where the string travels!
If you mark with a pencil at brace (like Eric says) and full draw you will see a sort of fan shape where the string rubs, this needs to be relieved.
Those straight grooves are one of my pet hates, as they must cause a nasty bend and chaffing of the string at full draw.
If I'm being fussy I'd say the groove may as well extent out to the tip of the bow, as everything beyond the string is excess weight.
I realise we all do stuff differently, so apologies to those who disagree!
Here's a pic of a horrid Hickory bow before I re-worked it... it shows the fallacy of the string groove, the wood outside the red lines is just dead weight achieving nothing, so why have a narrow groove?
+1 on what Mullet says... that's what I've tried to illustrate in my top two pics. Make the cross section of the tip sort of tear drop shaped with the thin taper on the belly.
Del