Electrical – hide a transformer in a metal box in the cabinet

Yes, you can use a 40w transformer to power your 37.5w load. However, given the quality of these small power supplies, running at 90%+ all the time will cause heat and premature failure probably.

You will need to drive the LEDs at 12v. Running them at 15-18v (or anything over 12!) is a bad idea for the life of the LED. You will need to put a resistor on an 18v supply to bring it down. I'd recommend simply getting the 150w 12v supply. Wattage/amperage is different than volts, where you can use a higher powered power supply and the connected lights will only draw what they need (example: running a 12v 50w light bulb from a 12v power supply rated at 150w is fine. Running a 6v 50w bulb on the same power supply is not fine).

There should be no problems with extending the circuit as you suggest. Install another box where you need it, run the cable between the boxes, and hook everything up. I'd contact the local building department, and ask them if they would consider cable run on top of cabinets to be "subject to physical damage". I wouldn't think so, but not all jurisdictions are the same. If they say it is, then you'll simply have to use conduit to run the wiring between the boxes.

You'll also want to ask if they consider the cable "supported", by running it along the top of the cabinets. They may tell you that you'll still have to secure the cable/conduit with staples/clamps.

Aside from those minor possible issues mentioned, I don't see any problems with extending the circuit.