But planning is not the same as doing, and it never got done.
Recently however I noticed a huge specimen of the same plant growing in a pot. The pot was one of many containing a motley collection of sick-looking house plants, on the window ledge of the company I work for. The oxalis had obviously moved in, and made a take-over of the pot having smothered the less vigorous original occupant.
I could have asked permission from the Keeper of the Plants, but she was deeply engrossed in some spreadsheet. No point in disturbing her for such a trifling matter, so into my courier bag with the pot. This plant was swiftly liberated, destined for important food-crop research duties.
At home, washing off the compost, I was slightly disappointed to see not one large edible tap root, but many small ones; what appeared to be a huge plant was in fact a colony of individuals, each with several edible roots of average length 30mm.
It seems that good growing conditions simply increase corm formation, and subsequent natural vegetative propagation, without the individual roots increasing in size. In fact the resulting congestion is probably detrimental to root size.
Rubbing off the corms as they occur to keep the plant 'solo' might result in a larger root, but that's never going to be practical on any scale.
So it looks like repeatedly collecting and growing out seed while selecting for root size is the only way forward.
Vigorous, easy to propagate, shade tolerant, disease free, and tasty. Only the size is wrong.
For now, I've repotted some to increase my experience with the plant.
The others? Mmm, they do taste good!
Update, 4th August: a shot of the plant in flower...