hello!
the concept of the sequencer mode on the m1 was meant to stay there permanently - that eight track internal sequencer was one of its main selling points, making it one of the first modern workstation synths, which could be used to make a complete track including drums.
sound design and composing often were seperate steps of the process then, due to this reduced direct control in all those new digital equipment. in the era before digital, those two steps were more fused together as there simply were more knobs to turn on the analog gear.
so either if you use the m1 sequencer or sequence from the mpc i think there is no real need to go to any other mode. but that depends on how much you tweak the sounds while you compose. some people do lay some serious time and work just to get the sounds right.
sometimes i do that too, but most of the time i compose using fairly standard sounds as i write a lot of music for regular band setting so the instuments are often the same.
that is totally different if i do an electronic or club track - there the sounds are more important to be right from the start of the composing process.
for the most part i stay on the track program page on the seq mode and only change one page up to the track volume page to balance my tracks. and i tend to write very quick, one track after the other to get to a rough sequence running fast and then make some variations and a fast arrangement on the mpc. with that basic song i pick up other (real) instruments and start to improvise over that and see if i find some good melodies going.
at the end it all gets dumped into logic to maybe add even more sounds and maybe also vocals and to get mixed.
for your quirky acting m1 - did you do anything to it since you got it? reset it to factory settings? or are you first exploring the leftovers of the previous owner? one always should do that... sometimes there is hilarious good sound settings and sequences hidden in used gear that can be of great inspiration.
but doing a factory reset, (maybe a change of the battery if the synth seems to forget all its settings each time it is turned off) and setting everything right for the own usage is definately the next first step to do, because it has to work for you from now on.
read all the manual, even the sections you don´t need right now, because sometimes there is the bit of information that was missing in the big picture if you just read the parts that you needed.
old equipment can have hardware defects from old batteries to dry capacitors to broken keys, so be perpared to search infos on how to deal with that type of problems.
but the good part is that the m1 might be the most sold workstation synth of all times and so there is plenty of spare parts and knowledge around the internets.
something might not be right with your m1 if it is changing its behaviour for instance when its gets warm after some usage. also the round push buttons often get broken, mostly those with heavy usage like the start/stop button if the previous owners used the sequencer.
or there might be something not right with the midi sync settings on the mpc or the m1?
when i press play or playstart on the mpc i can freely switch between all pages of the seq mode on the m1 so that should be working.
so double check your settings again and see if you find something that might be set wrong. it is a bit like checking a car engine - is there fuel, is there air and is there a spark?
with midi - are the track channels set right, is the clock sync right, is there a midi loop?
that is the bare basics - some instuments offer way more functions than that and every extra function can be a cause of a another problem. even more so if you are new to this and look at the midi settings like one might look at a car engine and go "hm nice, lots of stuff here... looking good... should be working...". so even this small setup of only the mpc and the m1 has so many parameters than can be adjusted i totally understand how complex it can be when you start this.
oh, got carried away a bit here...
actually i had the idea for the one synth challenge after i made some quick sequences to test the hardware and there i used some drum samples on the mpc, so i did the same as you today...

and maybe i don´t have to restrict myself that hard, do i?
peace, jo