Myriad v3.6 uses Microsoft Jet Database backend (a.k.a. MS Access database) - so if you've access to MS Access you can open the databases and have a look.
I suspect the information you are looking for will be in the 'Station Log' database file - which will be <Psquared data location>\PSquared\Myriad\Schedule\Myriad3.mdb - assuming you have a fairly standard set-up.
In this file is a table called 'database' - which is a single table holding the content of the 'database' tab in the myriad front end. (There's also tables called Songs and Jingles - which I think are legacy hold overs from previous versions of Myriad, these tables are empty on the station database I've just looked at from a 'started out at v3.6’ system.)
This table has a field 'reference' which appears to be a uniqueID record for the table.
The similar song information will be in the Autotrack database as well, though this is more a more complex relational database job, with the Titles and Artists details stored in separate tables to the song cards.
If Filemaker has the ability to connect to a Jet database then you should be able to read from the Myriad database. However I would have concerns over connecting to a live Myriad database - if your third party software locks records on a Myriad database when the Myriad software is not expecting this to happen serious problems could occur.
I'd recommend working on a copy of the station database file - unless it is vital that the minute a new song is loaded into Myriad it is available in your Filemaker application, a scheduled task to make copy the Myriad database file every so often would suffice.
Probably around 10 years ago now, in early Myriad v2 days I did experiment with the idea of copying details of an existing record library database of many tens of thousands of CD / Vinyl tracks into the Myriad database so that they could be searched for in the 'songs' tab. I gave up on realising that adding thousands of extra records meant that Myriad took about an hour to load! I would have consider exporting the data the 'other way' in a similar fashion to what you want to do, if it wasn't for a huge amount of data manipulation that would be needed due to the naming conventions used on the legacy dos based record library database software.
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Myriad user since 1998, now custodian of dozens of Myriad,Autotrack, Powerlog and Scoop boxes of many different flavours.
http://www.philedmonds.com