I know this is a bit of an old thread but I just realised something which will help, if you do return.
If the fist op-amp (the one on the left with the output connected to the square wave output) is replaced with a comparator (LM311 or LM293) the maximum output frequency can easily be increases without using a state of the art op-amp. One of the reasons for using a good op-amp was to ensure a fast rise and fall time. A comparator would solve this problem, but it means using an extra IC, although it should be cheaper than a top of the range op-amp. Note that the output for the comparator will need a pull-up resistor: 1k should do.