What I would like to do is write out Sl and Tt obtained from these files from many directories to a single file. So for example if I'm doing this for 10 directories I would have 10 entries in the file where I write these values to.
spacebar is right, but to fulfill your requirement of many files, you need to supply a number of files, like awk '...' DI*.DAT . Depending on your directory structure, you may want to use e.g. find to obtain all filenames applicable.
Then, in your command, only the very last occurrence of Sl.*thickness in the last file will be reported. If there's more of them, adapt your code. To report every single occurrence, make it