... why not let the rice the iberian muslims imported in the 10'th century, spread after the reconquestia northwards getting a slightly more cold resistent plant among the way ... much easier than fetching them half a year of transport away.
Except that the original rices Iberian Muslims imported were long grain African and Indian varities that can't survive north of the Metiterranian basin. They are extinct in Spain itself and their only descendents are in Portugal, Mexico, and Brazil. The varieties used to make Paella are the descendants of Javonica varieties that were encountered during the conquest of the Phillipines, and do not predate the 1570s in Spain itself. And those can't survive north of the Mediterranian basin either.
The Itallian varieties are first mentioned in 1476 in Venetian and Milanese records. However, the way that they are mentioned implies an already mature cultavation process that couldn't have made them a complete novelty. Molecular studies indicate that Arborio is a local mutation, but Bomba and Vialone Nano seem to be descened from a formerly obscure Yunan short-grain strain that has been previously sold by Lotus Foods and Urban Accents. Unfortunately, those can't survive north of the Mediterranian basin, either, not even Carnaroli, which was created after WWII by crosbreeding Arborio with Japanese rices.
Oh, and the basis for my arguement about rice in the British Isles are the Korean provinces of P'yŏng'an-do, Hamyong-do, and Hwanghae-do, the three northermost provinces, and extremely mountainous and subject severe Siberian Clippers. Until the Korean War and the subsequent rule of Kim Il-Sung, they were considered the breadbasket of Korea.