Hi Ian!
Welcome to the Thorn Cycling Forum!
I'm sorry to hear you've been having shifting problems with your tandem's front derailleur. Tandems can be a bit "special" when it comes to shifting problems because of the long cable and housing runs that can result in greater friction. Too, the power demands of two people add to whatever problems might be present.
I can think of several contributors to the problem and one indirect solution, all of which solved the shifting problems on my own tandem:
• I suspect the housing may be a problem, even though you mention replacing the cables. I found the real solution for me was to replace both cables and housing to minimize friction. In places where there were open runs (my Burley Rock 'n' Roll tandem routes the cables inside the frame...and used the frame as the housing for much of the distance), sheathing the cables in Teflon-Delrin liners did the trick. Look carefully at the problem...I'm guessing the problem comes not so much when pulling on the shift lever, but on releasing the tension and depending on the derailleur springs for downshifts. That can be a sure sign of excess friction in the system.
• Depending on the front chainline, it is possible the chainset (however many rings there are) is set too far inboard or outboard for the front derailleur to make a clean throw within its limits each way. If you check the SJSC website listings for "Thorn", you'll see they've developed a really clever means to address such problems. There is a spacer that also serves as an eccentric mount to place a front mech with 35mm clamp on a smaller seat tube. This can get things shifting up front while avoiding messing with the chainline.
• After replacing my cables and housings and fitting the liners where there hadn't been any, the final solution that broght great front shifting to my tandem -- even under load -- was the N-gear JumpStop:
http://n-gear.com/ It is an overshift catcher that allows one to adjust the front mech past its inner stop; the JumpStop catches what would be an overshift and ensures the chain settles on the small 'ring. Best of all, since it solves the inner/small shift problem, it leaves only the outer/big shift to deal with, taking care of half the problem. The upshift commonly occurs by pulling on the lever with a low-normal front mech, and is much easier to manage than downshifts, especially when dealing with the efforts of two people, as on a tandem.
• As a last thought, it might be wise to check to see if your front mech is "sized" to match the chain you are currently using. If you are using a derailleur meant for, say, 7-speeds and are currently running a 9-sp cassette and chain, the derailleur can fail to make clean shifts...just as you are experiencing. The "gate" is simply too wide to push the chain cleanly onto the next chainring. The SunTour front changer is from earlier days, and may not be a match with your current rear gearing or (more importantly) chain. Worth a look to see.
• If you need to replace the front mech, the standard-issue Shimano Deore front mech is solid and reliable and a good value. I went with a bottom-pull/top-swing model on my tandem and it works great, all for the princely sum of USD$8 at an REI season's end sale. eBay has them on offer for good prices as well.
Hopefully, something in the above will help. Good luck, and give a shout if these suggestions fail to help.
Best,
Dan.