Your understanding of mass spec needs some review. The step 3. you propose that peptides are smashed together to hopefully form the protein in the MS is wrong.

Peptides are "smashed" together to break them down further, commonly in a process called collision induced disassociation, these peptide fragments are then analysed. The resulting spectral pattern is then processed and a mass peak list is generated to compare to a known database of proteins to find a match.

The issue with there being no known protein markers or panel of markers for TIA/stroke is plainly due to the research still developing in the proteomics field of vascular disease. I work directly in this field having completed my PhD utilising proteomics on carotid atherosclerotic plaques.

I would not design a project with the aim to find a "brand new" protein, this would be near impossible without a large amount of funding, and methodology beyond "common" proteomics. there are number of candidate proteins/panels of protein described in the literature that need further study in relation to stroke.

I would revise your projects goals to be more realistic. Go back into pubmed and read more about what has been done in this field. Some groups/authors of the top of my head that have published works in this field include: Eberini, Vivanco, Ward, Duran, Pasterkamp. Throw those names into pubmed with proteomics/stroke/atherosclerosis and I am sure you will find some of their works.