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.
Myriad user since 1998, now custodian of dozens of Myriad,Autotrack, Powerlog and Scoop boxes of many different flavours.