"set a budget with my contact info and then ask them to call me or contact me when a cabin came up within that price range."
I do not know if they would accept that type of booking, or how that would work out. I have a feeling that IF they allowed that contract, you would fall through the cracks, and that even if the price range came down to where you want it, they may forget to call.
For that level of service, I would go with a good Travel Agent. And Yes, we make our deposit and then our TA does keep an eye out for us.
But the other half leaves nothing to chance, and still monitors for price drops.
We never pay the full cruise bill until it is time for Final Payment.
IF. as long as where you are on the ship does not bother you, then you can wait them out and hope for the best.
You can also book a "room Guaranty" this means that you pay the down payment for a particular category of cabins. ( for example, Inside cabins) That is usually a bit cheaper option.
One drawback to that is that IF that category gets almost full, then you could end up with the worst cabin location. On the other hand, we have known people that got bumped up to a higher category for the same cost.
It is a roll of the dice.
We once ended up right by the anchor. It was a great wakeup call when we pulled into ports.
