Do you REALLY mean FR-4?
FR-4 is a multi layer PCB material made of 0.25mm fibreglass layers impregnated with epoxy resin with multilayers laminated together. This sounds "unusual" as an FPGA encapsulation system.
(1) Patience and a "Dremel" with a high speed abrasive wheel (very fragile) works wonders on almost anything known to man.
(2) If you DO mean FR-4 and you don't mind some to much physical stress on the product during dismantlement then Methylene Chloride * will happily attack the epoxy.
The glass fibre is a tougher challenge but the MC epoxy attack will tend to rend it. MCV attack on FR4 is liable to be slow.
Don't expect the device to operate thereafter.
DO read the Methylene Chloride MSDS several times slowly (or several of them).
Use under a water layer is recommended.
Not breathing while using it is a good idea.
A sample Methylene Chloride MSDS
Note the use of the word "cancer".
Causes irritation to respiratory tract. Has a strong narcotic effect with symptoms of mental confusion, light-headedness, fatigue, nausea, vomiting and headache. Causes formation of carbon monoxide in blood which affects cardiovascular system and central nervous system. Continued exposure may cause increased light-headedness, staggering, unconsciousness, and even death. Exposure may make the symptoms of angina (chest pains) worse.
May cause irritation of the gastrointestinal tract with vomiting. If vomiting results in aspiration, chemical pneumonia could follow. Absorption through gastrointestinal tract may produce symptoms of central nervous system depression ranging from light headedness to unconsciousness.
Causes irritation, redness and pain. Prolonged contact can cause burns. Liquid degreases the skin. May be absorbed through skin.
Vapors can cause eye irritation. Contact can produce pain, inflammation and temporal eye damage.
Can cause headache, mental confusion, depression, liver effects, kidney effects, bronchitis, loss of appetite, nausea, lack of balance, and visual disturbances. Can cause dermatitis upon prolonged skin contact.
Methylene chloride may cause cancer in humans.