Just my 0.5 cents ... I think the Axoloti is the wrong platform for that type of application. The Axoloti excels in it's dedicated task of creating patches where audio is whisked around, and especially the capability of writing your own objects. However, when starting to do pure MIDI processing the paradigm of having objects which are essentially called upon 3000 times per second to generate 16 samples of audio isn't really ideal.
For that type of a application I'd recommend Midibox (ucapps.de). It's a lot more programmer based, i.e. there is no graphical patching environment at all (even though there is a nifty MIDI connected debugging environment), but if you're going to create an Electron-style sequencer you'll be doing mostly programming anyway. The disadvantage with Midibox is that you have no ready made hardware with built in MIDI ports, although it is easy to build your own starting with an STM32F4DISCOVERY board from ST. And if you're content with USB, you can use the on board USB port on the DISCOVERY board. Midibox takes the drudgery out of all the low level stuff, and basically delivers MIDI and timer events to your application and allows you to send MIDI events with no hassle.
I haven't written a sequencer using Midibox (although there are several examples on the ucapps.de page), but I needed a small MIDI processor a while ago which could provide octave shifting for my master keyboard controlled by MIDI program change messages. Once I had the hardware (which took a few days to build, based on the ST DISCOVERY board), it took about a full day of programming to familiarize myself with the Midibox environment and create my MIDI processing application. (I thought I'd uploaded the code to github, but it doesn't seem so, will have to get around to that some day).
It would be nice if someone had made an Axoloti port for Midibox, don't know if that's been done.
As for writing a sequencer in two months (assuming you're working full time on it), depending on your skill and ambition level I'd say it's definitely doable, but if you're just starting out in programming there are probably too many hurdles to jump over if you want a complete and professional (i.e. bug free) sequencer in that time. I've written sequencers in far less than that time, but with fairly rigid limitations.