A few points here:
first of all, the tag "bicycle=not specified" is not used anywhere else according to taginfo. this means that this is something you made up, there is no community consensus on this and thus probably shouldn't be used. there is also the fact that if there is not sign explicitly not allowing bikes on a way the assumed value is that it is the same as the normal access on the way. for Miami dade the defaults for public sidewalks is "access=yes".

the second issue is that you added access=permissive on way 1144585259 which is in the public facing part of the zoo so would in actuality be "access=customers;employees" because that way is only allowed for customers who payed to get in to the zoo and employees of the zoo. 