I think, it would be better to select the ortholog gene first. Because, there are several websites readily provide orthologs between monocots and dictos using gene id's. Few websites are,
Once you select your ortholog of interest, you can simply say the gene's preceding region (~2K bp) might be the ortholog promoter. Next, you can compare your interested region or whatever.
To find an orthologous gene might be a good approach, however that does not guarantee that the promoter of the orthologous gene is the same, in the best could be similar in the amount of regulatory boxes. First of all, I suggest, characterise the amount of regulatory boxes and its distribution and couple these information with the expression pattern of the gene that is regulated by this promoter. With this information you will have a better understanding about the promoter activity and then try to relate with other promoter with similar activity.