First of all: I want to make sure not to appear as smart-aleck due to the following, and do not want to bother other people with the following either. We all have our special knowledge which differs from person to person. And that´s fine because that´s why we can learn from each other and that is how it should be, IMHO.
(I assume you, Bruce and a lot of others wouldn´t get me wrong, even if I didn´t say this, but I don´t want to be misunderstood by anyone.)
The other key identifyer relates to veins M and Cu2 on the front wing which are not visible in any of my photos.
Well

, on your photo posted above M and Cu2 are clearly visible.
So the mayfly should be an ephemerid and belong to the genus
Ephemera.
There are a few
Ephemera species which differ in the markings on the dorsal side of the abdomen, and I´m not sure that yours here is
danica. Does your field guide list e.g.
vulgata? (To my knowledge it´s not to difficult to distinguish between the
Ephemera spp. but many other Ephemeroptera have to be examined microscopically.)
Let me put it like this: Often people with an interest in nature start with a closer look on birds (as did Bill Oddie, perhaps you too, Bruce and I, myself ) and therefore are familiar with the well known birder´s field guides, such as "Peterson, Mountford, Hollom" for Europe. In birds and with these books it is possible to identify the bird you encounter to the species since the whole avifauna is listed.
In invertebrates (and a lot of other creatures), because of their often enormous diversity, it´s different in the majority of cases. I don´t know the book you cited , but generally popular field guides on insects, unlike field guides on birds, do not include all species that occur in the region they cover. Often they only show one species that is common, conspicous etc. from a larger group (such as genus or family) but don´t give the information that there are other very similar species. This is misleading, especially when our promising eager naturalist, who started as the above mentioned birder, now tries to transfer his experience with the birder´s guide books to the field of insects or other invertebrates that is new to him. The popular guides are useful for a first general acquaintance with a group of such creatures. But In many cases one can´t identify a species or even genus reliably by comparing it to a picture in one of these popular books or often questionably labled pictures found on the internet. Instead one has to use an up-to-date key that has been put together and published by an expert of the group and needs a microscope, good lighting and some training in morphology. And sometimes even that is not enough and then methods of molecular genetics have to be applied to differentiate species.
So, at the end of the day, my only intention is to raise caution about labelling with scientific names. I recommend to cite a species name only if one is very sure of it. Otherwise it is a better proceeding - and no shortcoming at all - to label a specimen/photo only with the name of a higher taxon one is very sure of ( e.g. a mayfly, Ephemeroptera, or an ephemerid mayfly or an
Ephemera sp.)
Best wishes,
Betty