My wife and I (with the help of my underage son) have been installing new oak hardwood in the kitchen and lacing it to the existing hardwood in the dining room.

To tell the story from the start, the existing flooring runs perpendicular to the joists. The kitchen had tile originally, so we ripped that up and the 1/4" backer board (that was NOT a fun ordeal). After getting most of the construction adhesive and the MILLION screws out of the subfloor, we started adding flooring to the existing floor of the hallway that ran parallel to the kitchen.

After getting approximately 2/3 of it in, we are lacing the last few rows in the dining room and found that the dimensions of the openings to lace the new wood varies. The opening is slightly wider at the closed end than the open end. We've modified boards but still either get a bad warp (tenting from the tension when forced) or get a huge gap between the new board the existing boards on either side.

Any help would be appreciated.

Not much you can do about the situation unless you can completely remove the remaining existing area and proceed from there with all new material. That seems to be a simple solution. Have any pictures to share?

sounds like you weren't square and true when you started.

sometimes you need to follow the spacing with your new materials.

if you install everything tightly, you can end up with large gaps as you move along.

from what you have mentioned sounds like you may want to cut the stagger pattern further back..this may help if the boards were whipping when originally installed..simply said the original floor may not be strait..
check it with a chalk line.