Distributism was devised in the late 19th or early 20th Century as a distinctly Catholic economic system in which the "means of production" are distributed widely rather than concentrated in the hands of large capitalists or the government.
To put it in Biblical terms, everyone has their own fig tree.
Such a thing would limit the efficiencies brought about by economies of scale and I doubt it would be viable in the long run.
(The closest I can think of it being implemented in OTL was Mugabe's breaking up the white-owned farms into subsistence plots for war veterans in Zimbabwe and that's been a catastrophic failure.)
However, that's not important. What's more important is how we can get someone to actually implement a distributist economic system.
Maybe Mussolini is killed in WWI and someone survives in his place and we get a distributist economic model implemented in Italy?