Identifying Promoters in Non-homologous Sequences within the Same Organism
Why does the same promoter within the same organism have such varied sequences?

While there may be other reasons, the fact that the same species has several genes encoding GPD proteins is an indication that this enzymatic activity is important for different mechanisms, times or conditions. For example, I mentioned in a comment to one of your previous questions that the three GPD-encoding genes in budding yeast (TDH1, TDH2 and TDH3) are expressed during different growth phases. Therefore, although the proteins encoded by these genes might share both sequence homology and function, their promoter regions most likely will not. We even expect their promoters to be different, to allow for such differential expression. Put differently: if the three TDH promoters were all highly similar, we would expect them to also be active at the same times, effectively rendering the three genes redundant.
There is therefore no reason for assuming that promoters driving the expression of two different genes will share any homology, just because the encoded proteins happen to share function.

If the promoter sequence varies even within the same organism, the how can anyone extract the promoter with certainty since the organism may carry a different sequence for the promoter?

The only way of knowing exactly what region upstream of a gene that regulates it's expression (i.e., what functional elements that defines its promoter) is to characterize the promoter region. This is way beyond the scope of your work. What we tend to do in budding yeast when we clone an uncharacterized promoter, is to simply take 1000 bp upstream of a gene's start codon, and assume that this includes all elements necessary for proper regulation of the gene in question (e.g. possible transcription factor binding sites (TFBSs), transcriptional start site (TSS), etc). 1000 bp is a relatively safe length in budding yeast, since the distance between genes rarely exceeds this, and we tend to assume that promoter regions don't overlap neighboring genes' coding regions. But this might be different in your species. Also, if you know the location your gene's TSS, this would be a safer reference point than the start codon.

Generally, I'm trying to find the GPD promoter for P. cubensis (or any strong promoter) and clone it for use in my plasmid for transformation. I'm stuck as to how to go about finding a suitable candidate.

My guess is that the authors that cloned the GPD promoter from Lentinula edodes either already knew that this specific gene is highly expressed and therefore selected its promoter; alternatively they might have cloned all GPD promoter variants, and then simply published the one that they saw worked best.
If you don't have any information about the expression of the GPD-encoding genes from your species, any decision as to which promoter to choose will inevitably be more or less guesswork. It seems to me that the evolutionary distance between Lentinula edodes and Psilocybe cubensis is way too large to make any direct inferences. Nevertheless, with the lack of better options here is what I suggest:

Try to identify which of Psilocybe cubensis's GPD proteins is most similar (in terms of sequence homology) to the protein the authors chose for their Lentinula edodes GPD promoter. This might indicate that these are direct orthologs, and with a bit of luck may also share similar relative expression patterns and/or levels. You could also do a similar matching with the Tdh3 protein from budding yeast, since TDH3 is indeed a very strong promoter (article behind paywall, but easy to find elsewhere). If you still don't know which of the promoters to choose, proceed with both candidates and see which one works best (although that means doubled cost and effort).

Once you have identified your candidate GPD gene, you define an appropriate region upstream of your gene’s coding region as the promoter region. This can be arbitrarily picking 1000 bp, or the entire intergenic region, as @Cholpisit suggests.

Design your primers for cloning this region into your target vector, upstream of GFP.