A quick analysis of the English versions.

They preserve remnants of 17 of the 23 reconstructed stanzas. The best preserved version is that of Mrs Joiner which preserves 6 full stanzas close to the reconstruction despite losing 4 stanzas at the beginning. The best preserved stanza is the 16th of the reconstruction which is the description of his body and her kissing him. In general the English versions mainly preserve the middle block of stanzas 10 to 17 from the brothers' return to her lamenting over the body. Those English versions that have an ending telling of the brothers' punishment tell of them being tried and hung and there is no mention of them being drowned at sea in a storm. The English versions generally have their own autonomy and if pushed I'd say there was probably a shorter printed version following the original with a few alterations such as condensing the opening and changing the ending.

The next step is to compare the English shorter version with what is contained in CFS.