This is a complete vicious circle. He is staying home for feeling mildly ill as a direct result of staying off too often for being mildly ill. It's your son's responsibility to break out of it - only he can do it and improve his attendance to such an extent that they WILL trust him again that he is being genuine when he says he's ill. You wouldn't believe the amount of kids that try it on all the time in secondary schools. How are staff supposed to weed through the queue of malingerers, wimps and whingers to sort out the genuine cases? What they do is check their medical file to see if there is any long-standing medical conditions, liaise with head of year to see if there are any pastoral issues and if neither of these seem to explain the increased absences then it is just assumed that they are swinging the lead and the illnesses are not genuine. Or at least not serious enough to stay off for.
It is relatively easy for experienced staff to spot when teenagers are exaggerating or feigning their illness. They usually know the kids fairly well. Someone who is never off and has a good behaviour record will always be believed without much questioning. This is what your son needs to do. SHOW them that he can be trusted to only stay off when he is genuinely ill. The only way to do that is to improve his attendance.
As the adult you're going to have to get him up before you leave. If he says he has a cold, then that's the point where you say to him "it's just a cold. Here's some paracetamol." Sit and watch telly till it's time to leave, it will have kicked in by then and you'll find you'll feel a bit better." At a push give him a note for PE so he doesn't have to run round a cold field feeling grotty.
The school should be phoning you when he doesn't turn up for registration, so when they do, you can say "he said he had a cold this morning and told him I wanted him in school. He doesn't have my permission to be off and is truanting, please mark him down as such." Don't take the attitude when they ring you "well, what can I do? If he says he is ill and doesn't come in then there's not a lot I can do as I'm not there." You will come across as too laissez-faire. You need to be asking the school's advice and asking how you can help your son, with their support, to improve his absence levels.
Re: the meeting, I would ring the school and explain your predicament. See what they say. Tell them you will speak to your employer and see if something can be arranged to enable you to attend, and get back to them immediately. If they see you are taking it seriously and doing your very best to be there, it will help school to realise what a supportive parent you are, despite your difficult work circumstances.
Of course, this is assuming that there are no pastoral issues or real medical issues goinng on. You need to sit down with your son and say he needs to be very open about what his issues are with school as improving his attendance is non-negotiable. Tell him that will be more easily achieved, and with least stress, if both you and school are aware of any problems that he may be reluctant to tell you. Also tell him that you are taking him to the GP to get a check up as lots of little colds etc is not normal in someone his age. Make the appointment and take him. You never know what it might throw up. School will see that you mean business about trying to get the attendance problem sorted.
Youcan do this, OP, but you have to mean business, to not take a hands-off approach because you are not at home in the mornings, and to fully engage with the school to show them that you acknowledge there is a problem and that you personally want his attendance improved.
At my school in a similar situation they actually paid for a taxi for a number of weeks until the pupil was back into the habit of getting up and out of the house on time each day. It was a success story. It was a possible solution that was suggested by the school when they saw how badly the parent wanted the child to attend on time, but felt she was struggling in getting Her child to do it.
Do your best to attend the meeting and to demonstrate that you want this sorting ASAP.