Mashing process question---when to pull the grain?

[DFWhomedistill]

I'm still a relatively new distiller and have done about 10 batches. I've been focusing lately on getting a proper fermentation and that has led me to taking a look at my mashing process. To frame my question, I've been making bourbons according to the "rules;" 51% corn, aged in new American oak, etc. After the mashing in process is complete I usually get 8-10% potential alcohol mash but I've not been able to get the fermentation process to run complete. After 5 days the fermentation seems complete but only has consumed about half the sugar at most so I'm getting about a 4-5% yield. I've done everything I can think of to get the fermentation to yield more; changing the acidity of the solution, different yeast types, aeration of the mash, etc.

What I think I'm doing wrong......I am fermenting with the grains still in the mash and straining them right before distillation. I've learned recently that whisky makers strain and lauter at the end of the mash process. Do bourbon makers do this? Would the presence of the grains in the mash keep the yeast from being able to consume a higher percentage of the sugar?

Any help would be appreciated before start another run.