It depends on who you ask. At one time the thinking was to bed the recoil lug and the 1st 2 " or so of the barrel. Roughly where you are now. Many have barrel contact putting upward pressure on the barrel near the tip of the stock for best accuracy. The Ruger MK-II, and Hawkeye do. But most people anymore free float the whole barrel.
And some gun builders full length bed the barrel to the stock. Kenny Jarrett used to and as far as I know still does. Done right I think either method can work. I just think it is easier to free float, than to get a perfect fit to bed the whole barrel. From what I've seen barrel profile matters too. A super lightweight barrel might do better full length bedded, or with some pressure near the tip of the stock, and a heavy target barrel might be better full length free floated.
I'd shoot it before doing anything else. More stuff gets messed up by trying to fix what ain't broke than anything else.