For the S-DD1, I remember reading that you can disconnect a single pin on the cart edge connector and that would let the cart boot on a console with a disabled lockout chip. I remember seeing this years ago, but I can't seem to find the page in Google right now.
edit: I still can't find the page, but I had the info saved on my PC. There's two methods. One, lift pin 86 on the S-DD1. The easier (and more easily reversed) method is to block a pin on the edge connector with a piece of tape. If you follow
this cart edge pinout, it's pin 56. My suspicion is that cart edge pin 56 in connected to S-DD1 pin 86, so either method gives the same result, but I don't have an S-DD1 cart in front of me to confirm.
There are some important notes though. Blocking this pin will keep the cart from being able to boot on a stock (unmodified) console. The author also states that "it will not always load on the first try but it will load more often than not."
Usually people don't simply disable the lockout chip in the SNES for this reason, they install a switch so you can turn it on and off. Also, another option would be installing the
SuperCIC in the console.
I don't know about the SA-1, but you could try blocking cart edge pin 56 and seeing if it works.