My Retirement - Looking for some Gardening Help

Planning my gardens and doing OK

About three years ago my children gifted me with a flagstone patio.  I had wanted one for a while but was not sure how we could do it or if I really needed one as I already have a very nice deck.  One day, when they expected me to be at work but in reality I had taken a vacation day, two of my daughters and son-in-law came over with tools, a truck full of flagstone and all the equipment and supplies that it would take to install a patio. I was so oblivious as to what they were doing that I had not even noticed the truck and Bobcat going down the side of my yard. My first thought was that they were going to install a rain barrel to collect water, something that I had asked for as a birthday gift.  I did not look out my back windows to see what was happening and told them I would leave and go shopping so that they could complete their surprise.   I called hubby and met him for a day of shopping.  When we returned in about 5 or 6 hours, the patio was almost completed.  It was just what I dreamed of, and it gave me another place for a garden.  My first thought was what to plant between the stones.  I went to nurseries, asked advise from friends and family and read catalog after catalog.  I finally decided between Irish moss or step-upon thyme.  I decided on the English garden look with the moss  and, per the instructions, I thought that there would be enough shade there for the plants to grow well.   I also tried some thyme in a few areas to see how that would do.  After putting in thousands upon thousands of seeds and many plants of Irish moss, I know I have made a mistake.  The patio does get about 2 hours of sun a day and last year with the terrible heat, the moss withered and looked like straw.  I had spent many labor hours and quite a bit of money trying to cultivate these plants.  They were watered down every day, but apparently even a couple of hours of sun does them in.   This is my third year of trying to dress up this space and I am asking for advice.  The step-upon thyme did look nice in the crevasses where I planted them, however, they over-grew and I thought they looked somewhat messy and not the appearance I wanted.  However, they did very well and did not turn to straw.  The thought of getting on my knees and pulling out 3 years of work does not thrill me, but I am not happy with what I have done. I also have problems with grass and weeds growing among the moss.  I spend so much time pulling out these invasive pests.  The weeds do not seem to sprout up in the thyme though or at least are not as visible..  Unfortunately, last year, I pulled out all of the thyme and planted them in other gardens. So, it is April and I am ready to start over and tackle this problem once and for all. 

I am located in Zone 6.  Any ideas?