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OK!
Folks, thanks a lot for the advice on posting (I have been floundering a bit :) ) If I haven't messed up (YET again!) then I shall have attached another picture which I had included only as an URL so far. I hope that helps. As John suggested, I attached it to a reply. (Silly me! Oh well!)
Thank you also for the advice and comments.
Tony, I take your points, but I didn't like the jizz for Bombyliidae. Trouble was of course, that some of the jizz for Tabanidae also wasn't good; the eyes and antennae for a start.
What REALLY was bothering me was that where I live now we rarely see any Tabanidae except an occasional Haematopota and maybe if lucky, a loooong-tongued lovely Philoliche in the mountains, but years ago in some regions we had bee-like Tabanids that taught us to slap quickly and unthinkingly, and they looked more like this one than anything I remember. But I cannot find any reference to those. Maddening!!! I'll probably see some in obvious documents and circumstances in two weeks time!
Meanwhile, of all the suggestions so far, the most persuasive was that of jorgemotalmeida. I take my hat off to anyone who could make out the venation; I certainly couldn't! I had asked my friend to try for better shots, but of course without much hope.
Now, I don't know whether Heptatoma is actually the right genus, or even closely related, but those eyes had been driving me nuts, and looking up Heptatoma in Google images did produce some with suggestive eyes, antennae, and furriness. So, while I am keen for more comments, my thanks to all, and to jorgemotalmeida in particular.
Now let's see whether thisw attachment works! I'll master it someday... :)