In your originally post, I didn't think that I found which operation-system you are using. In a subsequent post, I found that you mentioned Ubuntu (Reaper works in 32/64 bit OSX/Windows (I am not sure how far back in the OS versions it goes though). These programs I am listing are not able to work in Ubuntu without the Wine-emulator. Unless something changed as of this writing, Reaper is most compatible with Wine (when compared to Audition 3),
Wine Rating on Reaper 5.x, I would avoid Audition 3.0 all together though. Audition 3 cost like $350, Reaper is either $60 or $225,
Info on Reapers Licensing costs.
I used Audition 3.0 in the past. I am not sure about the piano key roll edit feature though in Audition 3.0 ( I stopped using Audition 3 back in 2011 for Reaper). There are a couple of things I didn't like about Audition 3 (maybe more, I just don't recall the others right now); not being able to select multiple tracks at once, 32-bit. Here is a link to the manual
Adobe Audition 3.0 Manual Download in PDF, MIDI Sequencer is Chapter 10.. I think that in order to obtain a copy, one would have to initiate a license transfer from a current holder (I am pretty sure the license is Perpetual on Audition 3, not this whole Creative Cloud subscription model), Adobe is no longer selling licenses to Audition 3.0, and I am pretty sure Audition CC doesn't have a MIDI Sequencer in it added back into it though (they rebuilt Audition in 64-bit, and not all the features have made it back from the previous 32-bit version).
As far as Reaper goes, here is a link to a discussion about MIDI Sequencing in Reaper,
Reaper MIDI Sequencers, with some slight variations on other topics in Reaper. Another plug-in for Reaper is on this page,
Js: MIDI Sequencer Megababy and other versions, I'd really look into Reaper for ideas. I tested it out (just visually, no sound) and watched some videos, and read some about the availability of features, I think there is probably even away to programmatically access parts of the MIDI Sequencers with Javascript, or even C or C++, or Python (I'd have to get back to you on that as I'd have to reread somethings that I am not able to get back into right now.). One could even start working with the Actions panel with the SWS Extensions to really have some stored macros with all the JS (Javascript) plugins that come with Reaper. I am not positive, but thought at least I'd mention that there is probably a path between Python and the Actions section to use midi to trigger active VSTi or other effects/plug-ins that a MIDI track/file is using.
I apologize for any errors or typos. I hope this post helps. At least this offers some more options to look into.