cardiodan,
I haven't seen you post in a while....
I do think you kind of know the answer.... It takes me a while to get my heart rate elevated on my cardio days where I don't lift weights prior also.
What I do is go really extreme for the first X amount of time and then I just slow down and my HR stays elevated and in the HR Zone for a longer period just like the days when I lifted. If I don't do that i waste too much precious time elevating it, when it could be in the zone for those 5-10 minutes.
that was nothing fancy and it was already stated in a few different ways with the other answers, but not sure there is any other way to do that. I think my technique to get elevated would be more of a HIT at the beginning then i just stay steady HR zone for the 45 minutes or so. good luck.