We made this transit last week, on Thursday. It took almost exactly an hour from landing at the domestic terminal to getting airside at the T4-S, with only carry-on. DH is 72 and has minor mobility problems so we weren't rushing. It involved one bus, 4 flights of escalators down, a tram, 4 flights of escalators back up, Passport control, miles of "retail space" and going through "security" again. The latter was pretty brutal. Lines weren't bad but both my husband and I set off the metal detectors even though we'd removed all metal we could think of (belts coins, etc.) so we got groped. I had a corkscrew confiscated even though it made at least 20 previous flights in carry-on with no problem. They tried to confiscate my husband's prescription cough medicine even though it was clearly labeled, then made him take a sip of it. (TSA in the US had told us they aren't permitted to do that because some medication could be dangerous if taken at a time not prescribed.)

The Iberia Club is nice, though!