The problem is that the declaration says that no rules should be made re: limiting these short term rentals...If you changed the Declaration (which is possible but difficult) this is much more easily enforced - if necessary by the Courts; if you only changed the Rules (which is easier) it is certainly possible to enforce. In fact your Board has a legal obligation to enforce the Rules.
I think there is a difference if someone is renting out their Unit when they are not present and someone renting out their spare bedroom while they are there. The former is clearly a short-term rental, one could, probably, argue that the latter is like having (new) friends stay overnight and being given a gift of $$ by them. In our condo we have a Rule saying that guests & visitors can only use our rec facilities "if accompanied by a resident' so one way to discourage rentals would be to actively enforce that Rule.
But isn't it a by-law restriction, rendering the clause void?