This isn't modern Platonism.

Ok, then its Geddesian Platonism ;) The easiest solution is to do away with the concrete dynamic objects as anything fundamental and just regard reality as a timeless Platonia . I thought thats more or less what Julian Barbour suggests.

http://en.wikipedia.org/wiki/Platonia_(philosophy)

A program is an abstract object. Particular copies of a program stored in your hard drive, are concrete.

The actual timeless (abstract) math objects are the mathematical relations making up the algorithm in question. But the particular model or representation of a program stored on a computer can be regarded as a concrete math object. And an instantiated (running) program can be viewed as a concrete math object also ( a dynamical system with input, processing and output).

These analogies are exact:

Space is to physics as categories are to math

Time is to physics as dynamical systems (running programs) are to math

Matter is to physics as data models are to math