I am working with barley instead of wheat, but I felt several comments should be made on your 'mutants in wheat' proposal. You probably have heard similar comments before and addressed many of them in the proposal. Thus, hopefully a few of them might be helpful. Because it can take several generations of inbreeding to isolate each mutant in a true breeding line, the cultivar in which mutants are generated can be critical. Photoperiod insensitivity and spring growth habit have many advantages.
Some cultivars are more suitable than other for certain groups of mutants.
Gene duplication makes identification of certain types of mutant extremely difficult because gene interactions are much more complex. Cell cycle and chlorophyll mutants, for example, should be much easier to study in a diploid. Landraces are an important source of mutant genes affecting agronomic traits. Vernalization and photoperiod variants are more likely to isolate for existing accessions than from treatments with mutagenic agents. The array of mutants produced by EMS can be cultivar specific.