Gapped alignment of sequenced data to a reference genome has traditionally been a computationally-intensive task due to the use of edit distance for dealing with indels and mismatches introduced by sequencing. In prior work, we developed Accel-Align [1], a Seed-Embed-Extend (SEE) sequence aligner that uses randomized embedding algorithms to quickly identify optimal candidate locations using Hamming distance rather than edit distance. While Accel-Align provides up to an order of magnitude improvement over state-of-the-art aligners, the randomized nature of embedding can lead to alignment errors resulting in lower precision and recall with downstream variant callers. In this work, we propose several techniques for improving the accuracy of randomized embedding-based sequence alignment. We provide an efficient implementation of these techniques in Accel-Align, and use it to present a comparative evaluation that demonstrates that the accuracy improvements can be achieved without sacrificing performance. Code is accessible in github.com/raja-appuswamy/accel-align-release.