Not exactly a Rieker pro, but did buy some in Greece this past fall while on vacation because of sore feet/blisters from too much walking in not-so-great shoes.
The Reikers are ridiculously comfortable and saved my feet during the rest of the trip.
I wear a 7.5 in Clark's, a 38 in Ecco, but am *normally* a US size 8 in most shoes. Just these two brands I seem to take a 7.5 (similar to how you take a slightly smaller size in Clark's as well). In any case, the Riekers in a 39 fit me well. Oh, and if it helps, my one pair of Danso sandals are also a 39.
In your case, you might want to try the 40's in the Riekers. I've never actually looked at their size chart, but the Euro 38 Reikers in the shop in Greece were way too small - nothing like the Eccos in a 38 on my feet.
Hope that wasn't too confusing a reply! Go for 40's first.