You have a few possibilities:

1. Get 48-38-24 (or something like that). Apart from Spécialités TA, Full Speed Ahead manufactures such cogs. I have a set of ramped and pinned 48-38 that would work perfectly well with STI shifters.

2. Change the rear crankset for the tandem equivalent of a LX or XT mountain cransket. You will need a different bottom bracket.

3. Many Sugino cranskets use 110/74 mm bolt circles, allowing you to have a 24 granny, but also a 34 middle ring. With a Sugino cransket, you could have something like 46-36-24. If you could find a Sugino crankset that looks fairly similar and that is compatible with your Ultegra crankset, you could replace the rear right arm and get a "new and improved" mixed crankset.

Finally, if you use something like 48-38-24 (or 26), I would suggest a different cassette such as Sheldon Brown's Cyclotouriste 14... which could also be cobbled up at home.

Another related issue is your derailleur and shifter. The Ultegra front derailleur is perfectly able to shift a 44-34-24 crankset if used with a bar-end or downtube shifter; with STI, some don't have problems but others find the shifting less than optimal. You wouldn't have any problems with 48-38-24 though.