OK, I think I understand what you're trying to say.

Let's deal with the constricted breathing, for starters. Deal with the obvious issues and make sure the bike fits you. If you feel cramped and unable to stretch out, your riding position may need looking at.

If the fit is OK, you may be doing what many new road riders do and rolling your shoulders forward, thus preventing you from opening your chest. Even though you are "bent over" your shoulders should be down and relaxed and your chest open.

As far as the feeling of lacking power is concerned, I'm guessing that is illusory. When on the road bike, try riding along with your hands on the tops and then move into the drops while maintaining the same level of effort. Your cadence, and speed, will rise with the reduction in drag, and you'll probably feel that you're pressing less hard on the pedals. Your HR may climb slightly, too, because there's a small energy cost to just turning the pedals faster. So you may feel that your CV system is working harder on the road bike than it was on the mountain bike, despite the feeling of pressure on the pedals being less. That's as it should be, in my opinion. Running the higher cadence will mean that you are actually putting out more power, even though the force exerted with each pedal stroke may have fallen slightly.

The issue here is what sort of efficiency we're talking about. In terms of generating the maximum amount of power for the lowest oxygen consumption, low cadences of about 60rpm are the most efficient. They're harder on the legs, though, the muscles tire. High cadences require more oxygen for a given power output, so the HR climbs, but they spare the legs, so ypu can sustain the same speed/power for longer. You're fit from running, your CV system can take it, so stick with the high cadence/low pedal pressure. You'll be faster, and stay fresher, for longer.