Are you sure you wired those converters the right way round?
Normal TTL voltages are 0 to 5V but you need a 0 to 3V3 converter on the Zero if they are being fed into normal pins.
I believe so as they power on and I can receive rs232 data normally from this speed radar gun we have.
It's a no-name Bi Directional RS232-TTL converter with DB9 connector on one side and 4 pins going to arduino to the respective pins for 5v, gnd, tx, rx. We also have a dfrobot brand rs232-ttl converter and same thing. Speed radar has an actual serial cable connecting to the dfrobot converter, and we have just ground and tx-out from gps going with bare wire into the db9 connector on pin5 and 3. Data receives fine.
No other issues other than when mains power to arduino is off, the power led's have a dim and fast-pulsed look.
Now that I really think of it, not knowing initially that the GPS is outputting 3v ttl level data and connecting it to a converter....do i even need a converter for it if the arduino already accepts 3/5v ttl level signals?...My friend is worried that if for some reason the gps is outputting 12V+ and my meter is too slow to see it?...
So far everything else has been essentially plug and play (solder and go) lol....but even though everything works, this minor 'glitch', if you will, I'm sure will play havoc on the ic's with prolonged exposure to inappropriate voltages.