Do they make that .308 rifle with a heavier target barrel of target length?No, old friend, that is the heaviest barrel they make in .308.
However, those little rifles are deceiving. That barrel is 22" long and has a heavy profile, measuring 0.662 at the muzzle. The entire rifle is only 37.5 inches from heel to muzzle. It's very compact due to the short length of the action. When I first showed the rifle to my brother-in-law, (who has a penchant for heavy barreled custom beanfield rifles), he asked me if it has a bull barrel. I told him no, of course, but we both agreed that if appears to be a very stiff barrel with lots of steel for stability. If you go to the Shilen website, and use their contour guide for reference, the Handi barrels appear to be something between a #4 and a #5 contour. The rifle weighs 8 lbs with the scope.
This particular rifle, like most of my recent rifles, is a pawn-shop rifle. I've got $125.00 in it. It shoots my standard .308 load (43.0 grains Reloder 15, 168 Gameking) into 1.5 inches at 100 yards. I don't doubt I could find a load that gets it into the MOA level of accuracy, but I simply haven't had the time to do much load development for it. It'll become a "grankid rifle" and one of them will wind up dragging it through thick-and-thin. Hopefully this summer, I'll find The Load for that particular rifle.