Rebase Co-Op Maintenance

A lump sum paid to the co-op by whom?

Maintenance is typically based on the number of shares assigned to the unit. A reset of maintenance to a lower level would require a reapportionment of shares in the building. If shares are being taken away from a unit (to reduce the cost), who would those shares be reassigned to?

I've often dreamed about being able to pay down my share of the underlying mortgage and having the associated principal / interest and future refinancing costs removed from my maintenance.

Emphasis on the "dreamed." It will never happen, and neither would the situation described in the original post.

Back in the early 1990s there was a bank which offered (and at least 1 coop took) a bifurcated underlying mortgage (which resulted in bifurcated maintenance payments). Part A was a fixed amount, but part B could be prepaid by any shareholder at any time.

With the goal of increasing your valuation? Great idea but mechanically likely impossible.