Hi Shallow
i have the same setup and my solution is to do all sequencing on Protools as well as the audio. I simply don't use the ASR sequencer at all.
You will probably find it easier to do it that way for any new work.
For transfering old work to the Protools sequencer, I am not aware of an export midi data function on the ASR (anybody? this woud be much easier if there is a way...)
so, assuming you have a USB midi interface.... I'd suggest doing it this way...
1. Set up a remote midi device (doesn't really matter what it sounds like for this process - any synth or drum machine, or even soft synth plugin in protools will do) and configure midi so that a track on your ASR sequencer triggers the remote device rather than the internal sound on the ASR. this is just a temporary step so you can hear that it is working and the midi data is coming out somewhere.
2. mute or disconnect everything else and route the midi so that it is going through pro-tools via a new midi track
(nb getting started with midi tracks on protools is tricky as it is very much midi architecture added to an audio system, so its not that logicial. Essentially, you need to understand the busses and set up each midi track correctly - seee the protools manual
3. press record on protools and play on your sequencer. This will effectively record a midi track of one instrument's performance exactly as recorded on the ASR.
4. Reconfigure the midi so that when you playback on protools it triggers the original internal ASR sound instead of the remote midi device.
5. Repeat for each track
nb without synching, you may need to select all the midi data in each track and bump it slightly forward or back until they are all back in time with each other.
I realise this is pretty labour intensive, but you will find the midi much easier to manage if you just convert totally to protools.
good luck