I cannot help you with the considerations you face in your case because I've never run seriously, however, I can tell you how my post-op cardiac exercise has progressed. It may give you an indication of what to expect or maybe not.
Before when I was healthy, I was only doing about 5K at about 4.5-5.0 mph.
After surgery, I started walking. In the hospital, I was making sure to take three or four 10 minute walks a day. I was released five days after surgery.
When I got home, I started walking up and down the block. About 6-7 days after surgery, I was walking the length of one block and back.
Two weeks post-op, I was walking around the entire block twice.
Three weeks post-op, I was walking for 45 minutes at a good clip - probably 3.5 - 4.0 mph.
Four weeks post-op, I was walking for 60-75 minutes at about the same pace.
After that I started on my treadmill and began to jog. I was doing 30 minutes at about 3.0 mph. I was on beta-blockers, which keep your heart rate and BP down. My bpm was between 115-130.
When they took me off the beta-blockers, I kind of freaked out a bit because the very next day, my heart rate went up to 1140-150. By this time I was doing 3.5 mph for 30 minutes, plus a 1 minute warm up and two minute cooldown (remember, I've been sedentary for almost a year due to symptoms, so I thought it better to play it safe).
It's now a month after the beta-blockers and I haven't raised the speed up because the high heartrate scared me a bit. My heartrate has dropped. Now I'm doing the 3.5 mph with a bpm between 130-140, so it is getting better.
I intend to start to get more aggressive, but I just had my 3 month echo and want to see if there's anything weird going on in there first. No sense pushing my luck.
Gary, I do not know much about the root replacement, but if they can do it without cracking your sternum, you will be back in business in no time if all goes well. If they have to open you up the same way they do with AVR, then perhaps my experience can help you to set some expectations for yourself.
Your likely in pretty good shape, so your recovery could be faster, but please don't push yourself too hard too fast. Don't fall into the trap of trying to get back to your healthy condition in record time. Your body needs time to heal - even if you physically in great shape prior to surgery.
When you get a chance, please let us know what is entailed in your procedure. I am curious if they use just a dacron tube in there or what.
Kev