First Red Label FG

These older (1966-mid 70's) sound great, although they're not always playable.

Can you post a picture of the brace under the fretboard just inside the soundhole?  I haven't seen many from that era without a serial number, but with Yamaha there's always an exception.  But, you are correct with the date, but that was probably when they made ths sides.  The guitar probably finished about a month later.

A little belly is normal.  But a straight edge across the top behind the bridge.  With one end touching the top, measure the gap at the other end.  Up to 1/4" (1/8" per side) is OK.  Unless there's a broken brace there's nothing you can do about it.  The plywood has probably been like that for decades, there's nothing you can do with compressing it for a few days or even a few weeks.  Months maybe.  

Years of string tension tends to make the neck tip up and the bridge tip towards the soundhole, making the soundhole area collapse, causing high action.  A Bridge Doctor might tip the bridge back but it won't do much for the action.  Only a neck reset can fix the neck angle.

Check the neck angle by putting a 24" straight edge on the fretboard and pushing it until it hits the bridge.  If it hits 1/16" or more below the top of the bridge the guitar needs a neck reset.  I like to see 1/16" above.  Anywhere in between can possibly be made playable by sanding the saddle or (CRINGE!) sanding the top of the bridge lower.  But, beware lowering the string height above the top can affect the tone and output slightly.  It's a trade-off.  A neck reset is the right way to fix it, but the cost is typically more than what the guitar is worth.  I do them for only $300, but the cost of shipping a guitar can be $125 each way.  Not cheap!

Post some pictures, action measurements, and the neck projection.