Everyone experiences things differently, but I live in a big city and grind the commutes on a regular basis.
I like to hammer it from the stops, and so forth, as you suggest. Coincidentally, also just switched back to a road bike after a few years on an MTB. To be honest with you I liked the extra ruggedness of an MTB on the city riding, but the Road bike is growing back on me now. It is no easier on the road bike really, but you average a slightly higher speed for the same amount of effort.
On getting burnt out though, sometimes the ride just catches up with you. Especially if you are doing that strength work on the weekends on top of it all. In my case, like clock work, about very 5 weeks I just get burnt out. Also, you don't really get to change your routine around like someone who rides stricly training type rides. Maybe if you don't depend on the bike, drive the car for a week, or ride easy, really easy, for a week, at maybe around 130 BPM max, like someone else suggested (resist the sprints - no matter what!). If you're like me after FORCING the rest, you will come back ready to Rock'n'roll.
Secondly, look up a good recipe for a sports drink you can mix up --> glucose, salt, flavoring, caffeine, or what-ever. Or buy one of the pre-mixed powders. You'll keep yourself more stabilized. I used water only for a bunch of years, but sipping on the sports drink, instead, after you are into the ride, will keep you feeling a lot better. It has some extra calories you'll have to watch, but if you are replenishing your stores as you ride it is far more likely you won't want 5 sandwiches when you get home, like I used to when drinking water only, instead of the sports drink.
Finally, good choice on checking with the doctor, no advice might compare to a professional looking you over. Good luck to you.