The problem I see is that removing this log jam isn't going to prevent the next one.
A better solution is one that does more than just pushing today's problem towards tomorrow.
Also, when the problem is difficult, I favor solutions where the customer is required to have some involvement. In this case, the museum and the museum patrons are in a position to have political and financial influence that extends far beyond simply paying for a one time job.
Repairing the railway well enough to use a railway crane is where I would start, and I would ask the museum to use its influence to accomplish that chore. That would take care of both this and susequent jams at that location, and it would also serve as a general solution that could be used for the other area logjams.
rScotty