If you are bent on 3600 psi then why not use oil as a piston like I mentioned? You can use it with a direct injection pump off an old diesel or any of a myriad of inexpensive hydraulic pumps or combination of high flow/low flow (high psi) pumps. To pump gas at high pressure, the demands on machining precision go up significantly and maintenance goes up as well (and price)., plus "stages" become necessary. A hydraulic pump can run for years, and solves lots of other "sealing" and separation issues.
3gpm@1800rpm, $100
Hydraulic Gear Pump GP F10 6 1 P C 3625 PSI 4000rpm New MP Filtri JP | eBay
Even that little pump will squish 127 cu feet of gas to 3600psi in 5 hours at modest rpm. Just need a high pressure accumulator tank (a tank with a top and bottom outlets would do) and some valves and a controller.
3 valves/solenoids,
1. closes off gas outlet
2. closes off hydraulic fluid return to storage
3. closes off low pressure natural gas supply
operation:
A. start/reset:
close 1, open 2 and 3. Incoming gas forces fluid back into storage.
B. when fluid is at correct low level in accumulator:
close 3 and 2, open 1 and turn on pump. Stop process when correct pressure is reached.
C. When fluid is at correct high level, go to A and reload accumulator with gas.
Main compromise is between solenoid switching life and accumulator size/cost.
Do you need a membrane/floating piston in the accumulator? Or does hydraulic fluid not care if it is next to methane? Either way, oxygen is a no-no in any cng system.