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Fulcrum coding combines a high-field outer Random Linear Network Coding (RLNC) that generates outer coding expansion packets with a small-field inner RLNC that combines the source packets and the outer coding expansion packets. This two-layer Fulcrum coding allows flexible decoding in receivers with heterogeneous computational capabilities. Fulcrum coding has so far only been studied for conventional dense RLNC, which randomly selects all coding coefficients, and only for a statically fixed number of outer expansion packets. However, the probability that the coding coefficient row of a newly received packet is linearly independent of prior received coding coefficient rows (a prerequisite for successful decoding) is highly dynamic. We propose to exploit the dynamics of this probability to reduce the computational complexity of Fulcrum coding. In particular, we vary the density of non-zero coding coefficients, i.e., equivalently, the sparsity of coding coefficients, and the number of outer expansion packets to keep the complexity low while maintaining a reasonably high decoding probability. We introduce the general principles of dynamic sparsity and expansion packets (DSEP) for Fulcrum coding as well as two specific example DSEP policies. Our evaluations indicate that DSEP Fulcrum can increase the encoding throughput tenfold and increase the decoding throughput 1.4 to 4.3 fold while achieving decoding probabilities that are typically less than 1% lower than the conventional Fulcrum decoding probabilities. We also find that DSEP achieves somewhat higher encoding and decoding throughputs than the CodornicesRq (Release 2.1) implementation of RaptorQ block coding for small blocks (generations) of source packets, while RaptorQ is substantially faster for large generation sizes. Furthermore, we develop and evaluate an elementary DSEP recoding mechanism that achieves a recoding throughput more than double the decoding throughput.