You should do a basic scaled layout drawing & tweak the widths for the bays & the equipment room. Once you have a visual of the proportioned scale layout you can adjust where needed. From your dimensions---off the top of my humble head it seems that there would be a way to make it work with a little creative adjusting. It is a lot harder to know until you get a feel for it from the proportioned sketch. Our bay widths are about 17 feet wide which might be on the extra wide side. They are also tandem which is another option.
In my mind I can't make it work with either the conventional side by side set-up or tandem bays. You can get five bays on the lot if you can put the building on the property line on one side.
I'm assuming the width is 111'. If you allow 15' per bay you use 90'. That leaves 21' for an eq. room and an exit around one end. I guess you could use 12' for the exit and 9' for the eq. room, but both would be too tight IMO. Perpendicular to the street is not an option IMO.