Are any organisms known to use meiosis I to create non-identical offspring asexually?
In automixy the meiotic cells give rise to diploid offsprings. This can happen by diploidization of the haploid cell (1n-&gt;2n), which will produce homozygotes or endomitosis prior to meiosis (4n-&gt;2n) which produces heterozygotes. Examples:


Cnemidophorus uniparens : 4n-&gt;2n 
Sphyrna tiburo: 1n-&gt;2n


I don't know of any case where there is fusion of similar gametes to form a diploid cell. It is difficult for two ova to fuse in natural conditions because the vitelline membrane has to be dissolved. 
Experimentally a haploid ES-cell can be fused to ovum to form a progeny. Haploid ES cells undergo diploidization and when injected in blastocyst, can develop properly (Ref). In fact haploid androgenic-ES cell line had been made in this study by injecting sperm into an enucleated oocyte. These androgenic-haploid cell lines can be fused to ovum to give rise to viable offsprings. 

Also see this question. Similar topic