I can understand that a few days of research could return a variable response for project completion, within reason and, for what you describe, that should be a few days or a few weeks at maximum.

What could throw this orderly view into the seeming conundrum you describe would be some workpalce and technology variables. The largest variables, for a project like this, affecting project completion time estimates include the following:

1. IIs the software source library(s) current and complete?
2. Are the compilers dependible and licensed?
3. Does your QA process include COBOL program maintenance?
4. Does your organization respect or degrade, as being obsolete dinosaurs, developers who know COBOL?
5. As noted above, do you have developers and developer managers who know COBOL and the applications being considered for modification?

If any items in the above list are unknown, uncertain or negative, then perhaps your developers are not lazy but honest. Walk into our shop with seveal hundred servers, dozens of web servers, app servers, database servers, security, fixed maintnenace windows, change freeze periods and any estimate you would give would be meaningless or career limiting, if you don’t know the application structure or have a mentor that knows this information and is willing to share.
Consider also that perhaps the developers/programmers may be distrustful of their systems or their management. Please don’t take that personally, since the responses you are receiving may likely have been influenced by your predecessors.

Good luck