Final answer:
The procedure that accelerates mRNA degradation is the removal of the 5' cap, which normally protects mRNA from exonuclease-mediated degradation.
Step-by-step explanation:
The experimental procedure most likely to hasten mRNA degradation in a eukaryotic cell is the removal of the 5' cap. This cap consists of a methylated guanosine triphosphate molecule that protects the mRNA from being degraded by 5' exonucleases. The other options, such as methylation of C nucleotides, removal of exons, methylation of histones, and enzymatic lengthening of the poly-A tail, either do not affect mRNA stability or actually contribute to its stability and proper function.