True, the Dutch connection to Spain is another avenue for exploration. Aleydis is one of those names, given it's spread of use, that really warrants a good investigation and it probably will only get it from someone like you investigating all the avenues thoroughly. It may sound daunting but honestly, who more motivated to get to the bottom of it than someone with the name? Greek and Latin dictionaries are there to help and I'm sure there's great resources in Basque around today as well as linguistic communities online that can help. I'd encourage you to delve into it and let us know what you find!