I guess this gives them a whole new set of potential leads that they could go on. Now they can look at who may have died around the days in question here. Check out if they had any prior criminal histories or have ever been noted to have operated among other well know thieves.

After that they can look into who may have been arrested or detained immediately following the theft as this person could have gone to prison for many years or even died in prison.

How about a disgruntled employee or maybe one who couldn't stand to look at the art anymore?...since no security devices such as a video camera (I don't know how sophisticated they were back in the day, they could have picked up grainy) or alarms went off...could have been someone even in their own security detail. It definitely had to be someone who knew the lay out of the building. That in itself would seem to lean towards somehow who'd known the lay out of the grounds. Maybe the janitor did it...lol.