New exact, analytical solutions are presented for the conservative part of a standard two-fluid (density plus vorticity) model of the scrape-off layer (SOL) which are of the travelling-wave type and describe the transport of large, machine-scale structures across a plasma cross-section (radially and/or poloidally). It is conjectured that amongst these conservative solutions (some extended throughout space, others much more localised) might be the ancestors of propagating coherent structures, known as blobs, often seen in experiments and numerical simulations of SOL turbulence. Several types of solutions can be obtained, capable of mimicking not only high-density blobs propagating outwards, but also inwardly moving plasma holes (structures with densities lower than the backrgound's). Besides their fundamental interest as conservative solutions of the equations describing SOL turbulence, these exact solutions have the added value of providing benchmarks for the verification of numerical algorithms, as is here illustrated. Having thus verified one's numerical implementation, a more realistic SOL model (including diffusion, parallel losses and a source of core plasma) is solved (by gradually adding the extra terms to the conservative part) to check whether these conservative solutions survive the full dynamics or not. They actually do survive (albeit enduring some degree of distortion, ending up by being eventually lost) for parameters representative of SOL plasmas in present-day fusion devices, thus somewhat vindicating one's original conjecture that they might be the ancestors of blobs. In addition, being actual solutions of the conservative part of the fluid SOL equations (and with the possibility of taking essentially Gaussian forms), there is no need to further justify their use as seeds with which to initialise (so-called seeded) simulations. A further characteristic that these Gaussian, blob-like conservative solutions possess is that they have intrinsic net vorticity (or spin), which is also believed to be the case for turbulence-created blobs.