In fact I've, more or less, succeeded.
I can't go into this now, but suffice to say I've started using my iPad as my main audio recording device.
This involved buying a microphone interface called iRigPre then plugging any one of the two microphones (one a big capacitor über mic, the other a good quality dynamic mic) I have into it.
The microphone positioning presents no real problem as it's held in an hilariously adjustable mic-stand.
Positioning the iPad is a different matter.
The lead from the iRigPre is quite short which means the iPad has to be within about a foot of the iRigPre which is attached to the mic-stand with a useless Velcro strap.
I considered buying a cradle that would hold the iPad and clamp to a mic-stand.
They cost about £30.
I stopped considering.
Looking at the pictures of the Littlehampton Beach Uke Jam, I saw the official Littlehampton Uke Jam Film Maker with her iPad clamped in an easel.
Easels are multifunctional and cost £9.99:
It's horribly pale and wan.
Some tea-staining and oiling later:
This set-up works well for me.
Everything's exactly where I need it:
Some ideas, though interesting in concept, do not work:
...but oh, how I wish they did.