I also have this problem Ian. My 11 year old viking tandem now has a 10 speed Shimano setup which has a huge range and is generally great. For now I still have the original 8 speed Altus ("SIS") front mech and corresponding Altus flat bar index shifter. My cranks are the 160mm length Thorn (SJS) tandem cranks broadly similar in configuraton to your Spa ones (ie 110 BCD). If I recall correctly the rings are from Spa..so essentially a very similar setup.
On some changes from big chainring to middle chainring the chain would just "ride" the teeth of the middle ring...clicking but not dropping onto the teeth .. which sounds like what you have.
That first 10 speed chain had had some bad crunches around the bottom bracket over time finally refusing to hold gears at all..while miles from home. By the roadside I discovered the chain was twisted out of true in one section and i used a thin allen key and a thin screwdriver inserted in adjacent chain links to twist it straight and get back home. I wondered how long it had been twisted but it certainly explained some of the weird shifts i had been having.
I have a new 10 speed chain and block now and all seems well with decent big to middle changes although the front indexing is clearly not really right with a quick "two down one up" being required some times
I am now planning to install a non index shifter for the front mech..probably an old Ultegra bar end shifter mounted on the flat bar "bar end" (if you see what I mean). I think using the old "original with cheap tandem" Altus left hand front index shifter is just too brutal on the chain. A non index shifter will hopefully be more gentle.
Not sure this is your issue but check chain twist !!!
I will be watching the thread with interest...great post...