Interesting the way places change their names and old locality names fade away. I can shed some light on the Reedy Creek name.
A big chunk of the gold field from Eldorado to Wooragee and including Beechworth, lay on the Carraragarmungee run (don't try saying that fast after a few beers). The lease was actually held by Agnes Reid for her sons (David Reid included). In her lease application, filed four years before the discovery of gold in the region, the proposed boundaries of the lease were described using various landmarks, including Reedy Creek, which was mentioned by that name no less than four times.
Hence, the Reedy Creek name precedes the Reids and the similarity of the names was merely a coincidence, though it would lead to much confusion over the years.
As has been suggested above, the creek and its tributaries have been described by various other names over the years, including Woolshed Creek, Eldorado Creek, Ready Creek and Read's Creek. Reidy creek is a relatively modern confusion. However, it is still officially gazetted as Reedy Creek.
The creek was first opened up by miners moving downstream along Spring Creek from Beechworth (which itself went through several name changes from Mayday Hills to Spring Creek and finally Beechworth) to where Spring Creek joins Reedy Creek just above Woolshed falls. On its journey, Spring Creek falls over Newtown falls in Beechworth and then through a second set of falls known as The Cascades. The rich alluvial area from between The Cascades and Woolshed falls was known as the Reid's Creek diggings, with the name applying to the locality and township that sprung up there, as well as to the creek itself. In the majority of the historical references, when miners refer to Reids Creek, they are describing the locality along this section of Spring Creek. Officially, this stretch remains Spring Creek today. The township of Reid's Creek stretched along this section of Spring Creek, but was mainly located towards the intersection of the Woolshed road and the Chiltern Rd. Adding to the confusion, the Reids Creek Post office was officially called the Reidford Post Office as there was already a Reids Creek post office elsewhere. The Reid's Creek cemetery was on the block of land on the other side of this intersection where some holiday cabins are now located.
The area below Woolshed falls was known as The Woolshed due to the presence of a roughly constructed shearing shed that had been built by another squatter (William Cropper) who, while droving a big mob of sheep though the area, needed to shear his sheep en-route. The township of Woolshed was located a little further down the valley near Native Dog Peak. There were at least three other distinct townships along the road to Eldorado, including Devil's Elbow, Sebastapol and Napoleon.
Sorry waffled on a little there. BTW, Those are some great pieces and much larger than the typical gold out of Reedy Creek You have a good spot!