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Cozumel has recently hired a new 'harbor master' who is hypersensitive to anything remotely approaching 'sporty' seas, he's very gun-shy, conservative, so the odds of having the harbor closed to diving due to 'weather' are MUCH higher these days then they used to be.
I believe that guy had a short tenure! I just got back from a week yesterday. Got in 5 days of diving in the worst seas I've been in, and I've been going 2-3 times a year for 25 years. Wind was ripping and we had some waves come over the rail of the Pango had to be 4-6 foot sea. Some Ops canceled on their own and some turned back after just a few hundred yards. I know last Nov. that timid harbor master closed the place with just a ripple. No way could that same guy let the boats out last week.
Anyway to answer you and what you want:
Blue angel hotel -- small comfy hotel on the water, pool, mini fridge, small sandwich shop, 15 min. walk to town, all rooms face the water.
Several dive ops pick up there or just a $5 cab to the Marina.
On site op is Blue Angel with rinse tank and place to let wetsuit hang. you take care of your gear. They have a few boats. but no guaranty unskilled divers not with you or on small boat. All depends on how many divers they have. they will not send out many boats if they can fill up just one.
Dive Op options. for guaranty small group (6-8) max several ops with the small fast boats
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Living Underwater and Liquid Blue used the steel tanks, only one boat so 8 max. These ops tend to have more experience divers due to cost.
Bottom time Divers, Dive with Alison, Tres Pelicaninos, Scuba Tony, Bluextsea, Dive with Martin all have the 6-8 max boats use AL80's nitrox available and give good service. Some will take all your gear rinse and dry for next day, some will not take the wet suit but they will take the rest.
No one can guaranty you that they will only have good divers on the boat as economics also play a part. Some ops will require you all to end the dive when first diver to reach 700psi and surface as a group. Others will either adjust the buddy system with like psi divers underwater or Some masters will take you up for the safety stop then they return to the group and continue until the last diver reaches 700. If you are good on air these are the questions you might want to ask the op.
Ops mentioned in my post will let you dive your air and computer. So you know, my op is Bottom Time, but I have been with all these ops over the last 5 years and they all are top shelf. Last week I dove with Bottom Time, Tony and Alison due to economics. These Ops can not go out with just one or sometimes 2 divers on the boat so they talk to each other and arrange something so you don't have to scramble to find an Op at the last