Hi Curtis, interesting question!
In a previous life, I have dealt with a mainframe renovation. Didn’t have LeanIX or similar tool at the time, we used a very complex spreadsheet instead 
We modeled multiple mainframe-based applications as logical conglomerates of capabilities (e.g. Repo, SBL domestic, SBL international, sub ledger, etc. - this was an investment bank) and mapped those to capabilities and to existing non-mainframe apps (i.e. integrations) and to business processes.
We actually focused on a subset of mainframe apps and created a roadmap to “peel the onion” in stages. The roadmap was made of multiple initiatives targeting specific processes and integrations to gradually move functions first and data later out of the mainframe.
It was challenging because even if the incentives were big (spiralling mainframe costs, dwindling expert population, difficulties in updating mainframe code for new / updated capabilities), the timeframes and costs were huge as well, putting pressure on budgets and the availability of those precious mainframe experts. Also, because of scope, we couldn’t tackle the mainframe as a whole, but that created potentially negative dynamics when other departments relying on different mainframe apps were afraid that us renovating our apps would mean increasing mainframe costs for them.
In those circumstances you cannot succeed without steady sponsorship at the highest level