DeepPolar codes have recently emerged as a promising approach for channel coding, demonstrating superior bit error rate (BER) performance compared to conventional polar codes. Despite their excellent BER characteristics, these codes exhibit suboptimal block error rate (BLER) performance, creating a fundamental BER-BLER trade-off that severely limits their practical deployment in communication systems. This paper introduces DeepPolar+, an enhanced neural polar coding framework that systematically eliminates this BER-BLER trade-off by simultaneously improving BLER performance while maintaining the superior BER characteristics of DeepPolar codes. Our approach achieves this breakthrough through three key innovations: (1) an attention-enhanced decoder architecture that leverages multi-head self-attention mechanisms to capture complex dependencies between bit positions, (2) a structured loss function that jointly optimizes for both bit-level accuracy and block-level reliability, and (3) an adaptive SNR-Matched Redundancy Technique (SMART) for decoding DeepPolar+ code (DP+SMART decoder) that combines specialized models with CRC verification for robust performance across diverse channel conditions. For a (256,37) code configuration, DeepPolar+ demonstrates notable improvements in both BER and BLER performance compared to conventional successive cancellation decoding and DeepPolar, while achieving remarkably faster convergence through improved architecture and optimization strategies. The DeepPolar+SMART variant further amplifies these dual improvements, delivering significant gains in both error rate metrics over existing approaches. DeepPolar+ effectively bridges the gap between theoretical potential and practical implementation of neural polar codes, offering a viable path forward for next-generation error correction systems.