When I used my paid version of Eagle, I had to buy the pro version of layout (where you actually lay out boards) – not because any of my designs were that complicated, but because I needed physically large boards.
Eagle, in their wisdom back then, wouldn't allow the standard version of schematic capture to work with the pro version of layout, and the pro version was $500. Instead, I used TinyCad for my schematics. TinyCad will export a netlist that can be massaged enough to import into Eagle, but it never worked that well. Differences in pin numbering on switches and similar components burnt me enough times to give up on importing a net list.
I laid out my boards exactly as I described above. Put the footprints on the board, make the connections using airwires, then arrange the parts and lay out the tracks. Tedious, but it works. I've laid out some fairly complex boards that way.
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