The way to ensure a casual game is accessible is to be dependable. That means you don't postpone the game due to schedule conflicts — that only punishes the players who could have made it, and makes people unsure if the game is even happening on a given week. Disappointment from willing players and doubt from uncommitted players kills casual games; you can't have a casual weekly game without a fixed schedule.
That is, of course, assuming that schedule conflicts are due to others' schedules and you're just falling into the trap of postponing when some of the casual players can't make it. That's a fine response for committed players, because they'll be back next week. With casual players though, that's how you ensure they drift away and forget about your game. With casual groups and a modular campaign, just run the game anyway with those who show up — and let those who can't make it that week feel left out and want even more to be there next week.
However, if it's your own schedule that conflicts, seriously reconsider whether you're able to organise this game. Specifically aiming for casual players requires extra work from the organiser, not less. It's necessary to carry the part of the game that they're not willing to, which is precisely making sure it happens every week you're physically able to. If you can't commit, you can't expect even less-committed players to show up, and should put this plan on the back burner until your life can accommodate the extra demands that come with organising a game for casual players.
I ran a weekly flexible-attendance game like this for several months, and it only kept its momentum because I ran it the same time and day every week. The only exceptions were when something unforeseen came up that made me unavailable (and I did my darnedest to minimise that). Otherwise, the game was on with whoever showed up, and sometimes that was as many as a dozen, and other times it was as few as the wife-husband pair who proved to be the solid core of the player group.
What's different is that you're hoping that others will run sometimes too — that's admirable, but you can't rely on it at first unless they're equal partners in this plan and want it to succeed as much as you do. If you're just hoping that casual players will fill in for you as organisers, you'll never get the plan off the ground. To establish the pattern you have to be prepared to run every week for at least a month or two, so that others can get used to thinking “oh yeah, it's JamesRinn's game night tomorrow.” Even if you have someone or a few others lined up to run games, you're the one invested in kicking this off and sustaining it, so be prepared to step up without complaint if the GM suddenly can't make it that week, in order to establish and then maintain dependability of the game.
At first, you may get more interest than actual commitment. That's okay — some people take a few weeks to adjust to a new weekly opportunity before they rearrange their weekly schedule or habits to accommodate it and make it to the game for the first time. So long as you've got a single player though, you can keep on making the weekly games happen, and that means the latecomers can trickle in as the weeks go by. The last thing you want to do is have the one night that someone can finally arrange to show up be the night that you cancelled because you didn't expect anyone to show.
It's very helpful to have a solo activity that you can do in that time slot that's related to the game — more preparation, related reading, etc. — so that you can keep the schedule even when nobody shows up. This means that not only are you reinforcing the dependability habit for yourself, but you're there and ready to go if a lone player shows up late but ready to play.
The keyword is dependability. When the group is casual, the organiser dependably organising it every week, regardless of attendance, is the only way it can get established and become a fixture in others' minds and schedules.
