How to handle letters of recommendation requirements in this situation? I'm wondering about the best way to handle the following situation. Some time ago I've asked my then-potential referees about possibility to become my reference sources and they kindly agreed, after which I've updated my CV with their contact information.

After some analysis of the academic job market advertisements, I had an impression that most institutions (at least, solid ones) do not expect receiving letters of recommendation directly from a job applicant, but rather from referees (via either e-mail, or online forms). However, recently I ran across at least several institutions (including some well-known ones), which, in their instructions, ask job applicants not only the traditional set of documents (cover letter, CV, samples of research, teaching and research philosophy, transcript, teaching evaluations), but also recommendation letters instead of references.

The problem is that now I have to explain this situation to my referees and kindly ask them to send me those letters of recommendation (for institutions, expecting them from applicant) plus to submit those letters directly to institutions, which expect that information from referees. Is it a reasonable request? My referees are very nice people, but quite busy, and I feel uncomfortable to bother them more than needed. However, I don't really see any workarounds in this regard. Is there anything else I can do to optimally solve this problem? I would appreciate your opinions.
Everything will be fine. If they have ever written more than a handful of these letters for others, they will recognize that different institutions have different requirements. Just tell them what you need, and thank them very much for their time and patience.