A valve for a well system including a valve housing including a first housing port, a second housing port, and a bore, a piston received in the bore and including a first end, a second end, and an annular flange including a first annular surface and a second annular surface both of which are in fluid communication with the second housing port, a piston seal disposed in the outer surface of the piston and in sealing engagement with an inner surface of the bore, and a cage assembly that includes a cage including a bore, a first cage port, a second cage port, and a third cage port, and a spool disposed in the cage and coupled to the piston, the spool including a throughbore.