First let me say this: I am no gardener. Every plant that enters my home or yard dies a slow death of neglect. I do have some experience trying to remove weeds from other non-weeds, and there is a practical aspect of "uproot every GMO plant" that I think may be impossible, but this is speculation. Let's get into a literature review.
A frequently cited paper is Dröge, M., Pühler, A. & Selbitschka, W. Horizontal gene transfer as a biosafety issue: A natural phenomenon of public concern. Journal of Biotechnology 64, 75–90 (1998). Table 3 contains the most relevant information about horizontal gene transfer between plants.
In situation number 1, consider that the rhizosphere (the area of soil around the root of a plant) is constantly populated with bacteria. These bacteria are shown to sometimes transfer genetic material to and from the plant, through the roots. Unless you somehow sterilize the soil after uprooting your previous crop, consider everything you plant in that field possibly contaminated.
Situation 2 is less clear, but Monsanto does sue farmers found to be using their seeds without a contract, and many farmers say this is because of cross-pollination. I think you should assume that your field will soon be contaminated.