Hey Vincent, regarding your question on removing the soldering of the InfraRed LEDs - it can be done and if done correctly, there shouldn't be any damage to the LEDs. The problem as cute_boboi pointed out is the antennas that receive the signal from the toll booth that triggers your SmartTag to start transmitting. I'm not sure if this signal is also IR or if they're RF signals but in either case, it'll likely not work well if you put the receiver somewhere deep in your car.

Here's a thought:
1. Lengthen the battery wire, solder it into a stripboard with an LM7809 and 2 capacitors then connect it by soldering some wire to an adapter for the cigarette lighter. This can be your permanent power source. The LM7809 will reduce the 12v from your cigarette lighter to a steady 9v into your SmartTag.

2. Desolder the buzzer from the smart tag and solder wires in its place then solder the other end of the wires to the buzzer. This is to offset the big buzzer from the tag allowing for a slimmer profile. Also you can get creative here by using lights instead of a buzzer or both etc. Also you can mount the buzzer or whatever combo you create anywhere you like in the car.

3. I can't be sure how thick the smart tag circuitry is from the picture but judging from the battery next to it, it's no thicker than a 9v battery. This means you can get the whole thing into a pretty slim casing - you can try getting any existing pre-made cases from electronics shops or you can craft your own using those pre-made cases. The name of the game here is to keep the thing slim but accessible. It needs to be transparent to let the IR through but the innards shouldn't be visible. Maybe you can reuse that dark plastic from the original SmartTag case? You also need to mount the smart card within the case using glue or something so that it doesn't rattle around in the case.

4. This is the part where it gets hard. We're working a line-of-sight restriction here where the transmitter (and probably receiver) must be line of sight to the reader at the toll plaza. 2 solutions I can think of are:
a. Mount the new case you've made behind the rear view mirror. The tinting would likely interfere with the strength of the IR light, so you need to remove some of the tinting. Since the front facing part of the case will also be dark, it shouldn't really ruin the aesthetics much but you be the judge of that. If you've made your battery wire long enough, you can get a mechanic or the body shop to run the wire through the ceiling material, down your A pillar, through your dash and to the cigarette lighter area.

b. See if you can get the body shop people to cut a slot somewhere near the front top surface of your dashboard where the windshield meets the dash that can fit your case tidily such that once your new case with the dark plastic top is in the slot, it looks as if the dark plastic bit was part of the dashboard. The grey dash / black plastic wouldn't look too messy if the slot is cut and shaped nicely. I'm not sure if the SmartTag works if it's pointed up vertically or if needs to point forwards at an angle. You can test it out with your normal smart tag if you wish by leaving it flat on its back on the dash and driving through the smart tag lane.
If you come up with a solution to the mounting problem, post it here! This is a good thread