I think this is a good idea. Let the current tenants know that you need a decision about if they are renewing at the higher rate or leaving within 60 days of lease end, otherwise you're not renewing. If they don't renew, start advertising at the 60 day mark. The better prospects do start looking a couple of months ahead of an anticipated move date.
My guess is that the tenants make a big deal out of the increase because they either feel the property is not worth more or they can't afford it.