Personally, I don’t find the Exodus passages to be extremely convincing arguments for a young earth. If the usage of yom in Genesis is indeed referring to a longer period, I don’t think it is unreasonable for God’s instructions to be of symbolic nature.
8 “Remember the Sabbath day, to keep it holy. 9 Six days you shall labor, and do all your work, 10 but the seventh day is a Sabbath to the Lord your God. On it you shall not do any work, you, or your son, or your daughter, your male servant, or your female servant, or your livestock, or the sojourner who is within your gates. 11 For in six days the Lord made heaven and earth, the sea, and all that is in them, and rested on the seventh day. Therefore the Lord blessed the Sabbath day and made it holy. (Exodus 20:8-11, ESV)
12 And the Lord said to Moses, 13 “You are to speak to the people of Israel and say, ‘Above all you shall keep my Sabbaths, for this is a sign between me and you throughout your generations, that you may know that I, the Lord, sanctify you. 14 You shall keep the Sabbath, because it is holy for you. Everyone who profanes it shall be put to death. Whoever does any work on it, that soul shall be cut off from among his people. 15 Six days shall work be done, but the seventh day is a Sabbath of solemn rest, holy to the Lord. Whoever does any work on the Sabbath day shall be put to death. 16 Therefore the people of Israel shall keep the Sabbath, observing the Sabbath throughout their generations, as a covenant forever. 17 It is a sign forever between me and the people of Israel that in six days the Lord made heaven and earth, and on the seventh day he rested and was refreshed.’” (Exodus 31:12-17, ESV)
It is not unreasonable to think that God’s instructions for the day of rest could simply be symbolic of “God’s day of rest”, especially since we’ve agreed that God certainly did not need a recuperation day. It would be a little silly to insist that humans had an era/epoch of no work, but perfectly reasonable for God to instruct for a day of rest as a symbol.
A similar situation can be found in denominational beliefs about the sacrament. There are not many denominations that hold to Jesus’ literal words of “This is my body” and “This is my blood”.