1.5 amp Bipolar Stepper Motor Driver?

I was thinking of using thermal paste in order to keep both chips at the same temp to try to get their resistances as close as possible

There is no benefit to that because you are raising the temperature of one or more chips to benefit one chip. You are effectively putting all your eggs in one basket. It is better to say " Every man for himself !" and let the chips fall where they may ( no PUN intended) . By separating them and using a proto PCB to dissipate heat, each chip stands by itself and dissipates "X" mW of power | where X = 1500 / n | n = number of chips in parallel. By using only 3 chips , each L293 will have to dissipate 500 mW. If n = 4, then X = 375 mW. In any case , it is wiser to let the chips stand on their own merit and not put all jour eggs in one basket with no heat dissipating device because then you are assuring they will run hot and possibly fail. With a proto PCB to separate and dissipate the heat you helping the chips survive instead of assuring their destruction. Look at the proto board. With 3 or 4 chips spread out you could even put small heatsinks on each chip ( if you can find or make them). The hookup wire itself is made of copper and each wire will absorb some heat. With all that wire going from one chip to the next and then to the breadboard , if you had a thermal imaging viewer you would see the heat travelling along the wire , dissipating as it goes. Just make sure you make wiring list of every connection and highlight it with a yellow marker when each wire is soldered. When you have things in parallel you have be extra careful.

electricviolin: I think I am just going to go with the stacking the chips idea. It seems the fastest way to do this (as long as it works, it is not really crucial how I do it). Thanks all!

Don't, please don't.

You need the right device for the job, not the wrong one(s).