+1 @draythomp for the improved sketch! Initially I could get neither that nor the example from the Grove Streams site to work. Both caused a "401 Unauthorized" to be returned from GS. Turns out the PUT url was not being built correctly; it may have been some evil with the Strings. Somehow I fixed it, before I fully realized what was happening. Seems to run quite well and no evidence of a memory leak after running several hours.
I did later remove some of the String stuff, although not the major parts, used F() to move some constant strings to PROGMEM, and changed to a fixed IP rather than DHCP and it now shows over half the SRAM available.
I have hardly begun to comprehend the web site but I really like what I see so far. This may well be the best fit for my needs.
I'll continue to work on the sketch with the aim of removing all String usage. I'll post what I end up with. Right now I have:
freeMemory()=1073
AVR Memory Usage
----------------
Device: atmega328p
Program: 20826 bytes (63.6% Full)
(.text + .data + .bootloader)
Data: 756 bytes (36.9% Full)
(.data + .bss + .noinit)