Bucket Priority Queues with large integers for $O(1)$ insert and extract~min?
Your proposed data structure is simply a hash table with some rounding to reduce the number of buckets. Effectively, all this does is divide the problem complexity by some constant factor (128 in your example). 

You have no hierarchy in your design, so there is no way to have O(1) access to the smallest/largest non-empty bucket. To achieve this feature efficiently, you're already pretty much bound to some type of priority queue. This class of data structures is well studied, and has various implementations with typically very low bounds on complexity.