Accurate automated tree crown delineation (TCD) requires highly precise boundary segmentation, yet reduced-resolution architectures face limitations from decoder outputs at lower spatial resolutions. We propose BARE (Boundary-Aware with Resolution Enhancement), a simple architecture-preserving training strategy combining external full-resolution loss supervision with class weighting. BARE upsamples decoder output solely during training, maintaining inference efficiency while improving boundary precision. Through comprehensive evaluation on SegFormer, PSPNet, and SETR using the OAM-TCD dataset, we demonstrate that external full-resolution supervision universally benefits all tested architectures, achieving significant boundary quality improvements. We introduce B-IoU (Boundary-Intersection over Union) to TCD research, enabling rigorous boundary quality assessment. Our systematic evaluation reveals architecture-dependent optimization characteristics, providing actionable guidelines for practitioners seeking to enhance boundary precision in reduced-resolution segmentation architectures via training-only modifications. Code: https://github.com/attavit14203638/bare .