Godfinger is an okay sniper rifle but you have to avoid Accelerate altogether. If you don’t it will take an absurd distance to get the max damage which is already significant without any sort of bullet speed enhancing skill. If you can be far enough away for all the bullets to spawn the Godfinger is hands down the most powerful NE sniper rifle in the game.
The Hawk Eye is actually a really good sniper rifle with how accurate it is and mild recoil. The downside to the Hawk Eye is that it is outclassed by Muckamucks, the Buffalo, the Elephant Gun, and it can eat through ammunition faster than most other Jakobs sniper rifles especially if you fail to get head shots.
As for the Invader and Morning Star I am not familiar with them enough to recommend or shoot them down.
If you want to stick with Jakobs you might want to try the Cobra which is a decent sniper rifle but becomes a bit of a monster if you have an explosive relic; it surpasses the Buffalo in terms of damage against slagged enemies. Problem is trying to get one and that you need an explosive relic to get the most out of it. Otherwise a good quality Muckamuck with matching parts will out damage the Cobra.
I still recommend the Buffalo as even in the OP levels it can hold its own even if it takes some getting used to. Anymore I prefer my sniper rifles without a scope than with one.