reverse polarity without relay

If all you are trying to do is convert (-) to positive you can use a PNP transistor rated for at least 3A. 

You would only need two relays to convert (-) to (+).  What kind of alarm do you have?

You can also get smaller mini relays that don't take up near as much space.  Another alternative would be a DEI 451M - two mini relays in one small enclosure designed to turn low current (-) pulses in to whatever you need them to be.

Here is the relay to convert...Would need one for each lock and unlock wire...You could also extend the wires and place the relays in another location...Really anywhere...Just extend the wires...

Convert a Negative Output to a Positive Output

If you have a switch or an alarm or keyless entry that has a negative output that you wish to use to switch a device that requires 12V+ such as a horn, dome light, parking lights, head lights, hatch release, etc., wire a relay as shown below to convert the negative output (trigger) to a positive output.

Run a 470 ohm resistor between the (-) out and the base of the PNP transistor.

You must wire a diode between the (+) output of the transistor and ground to protect the transistor from the inductive relay coil.

Seriously, grab a 451M and call it a day!

Don"t see why you would have to tear up anything...Arent you going to have to give it 12v-ground-and run the wires to the doorlocks anyway...? I was just trying to add some ideas why the relays would work fine...In case you overlooked those options... But i posted a link for the converters...Cheap...easy to install...tiny...Or follow the others suggestion with the dei piece.