Dense encoders and LLM-based rerankers struggle with long documents: single-vector representations dilute fine-grained relevance, while cross-encoders are often too expensive for practical reranking. We present an efficient long-document reranking framework based on block-level embeddings. Each document is segmented into short blocks and encoded into block embeddings that can be precomputed offline. Given a query, we encode it once and score each candidate document by aggregating top-k query-block similarities with a simple weighted sum, yielding a strong and interpretable block-level relevance signal. To capture dependencies among the selected blocks and suppress redundancy, we introduce Top-k Interaction Refinement (TIR), a lightweight setwise module that applies query-conditioned attention over the top-k blocks and produces a bounded residual correction to block scores. TIR introduces only a small number of parameters and operates on top-k blocks, keeping query-time overhead low. Experiments on long-document reranking benchmarks (TREC DL and MLDR-zh) show that block representations substantially improve over single-vector encoders, and TIR provides consistent additional gains over strong long-document reranking baselines while maintaining practical reranking latency. For example, on TREC DL 2023, NDCG at 10 improves from 0.395 to 0.451 with the same block budget k = 65, using at most 4095 tokens. The resulting model supports interpretability by exposing which blocks drive each document's score and how refinement redistributes their contributions.