Veni, Thanks so much for the detailed answer.
Have you enough to start - yes it appears likely but your language is a little vague in describing the relationships of tested relatives so I'm unsure if they fall into the "too close" category. But if you have further matches with more distant "known relationship" relatives you can work with their matching segments but there will be fewer of them.
I guess my details were not as clear as I thought. The relationships I was describing were of the test subjects to me.
I have the 4 siblings (myself, my brother and two sisters), our mother and her brother, as well as their (mother and uncle's) maternal first cousin.
A word of caution - one should be aware that some DNA matches may be related to multiple grandparents or if grandparents are related to each other (as in my case) one has to be careful that the known relatives used to determine the grandparents are only ones that are related via one grandparent.
My father is deceased but, I have two of his first cousins. I think this might be where the problem lies. These are my father's "double first cousins". Though as far as I can tell these are the only two of his generation still living. Since these cousins are related to both of my paternal grandparents, it would seem that I need to find someone who is only related to one grandparent. Am I understanding this correctly?
Thanks as well for the offer to help. I just might have to take you up on that!