Not being picky or anything But it is nice to have a fertility plan that reaches a few years in the future for hay crops.

Constructive advise:
When your alfalfa is first showing blooms, go out and clip a nice plant sample of only alfalfa. Clip the top third of top 6" of the alfalfa plants. Then the alfalfa will tell you what is the major limmiting element at that time.

Sulfur is an good possibility. That can appear much like a nitrogen deficiency.
Could be Molybdnium that will result in a real nitrogen deficiency. Warning that requires an extra effort by the Laboratory and will cost extra to boot.

Potash can be a suspect as it is essential in so many functions in the crop. Nitrogen effeciency one of them.

 Normally I would suggest you adopt a hay testing system to monitor soil fertility needs. The problem is for a mixed grass alfalfa product you are shooting at a moving target. It is a whole lot easier doing a plant analysis with all alfalfa, all timothy or all orchardgrass.

I really can not comment on soil testing and suggestions. I would use soil testing for liming. Usually to keep the pH in bounds.  It is possible that too low a pH can encourage what you are seeing.

Why 300lbs of 13-13-13?  In theory alfalfa does not require nitrogen.  If you fertilize for a grass hay the grass will crowd out the alfalfa. If you fertilize for alfalfa (no Nitrogen) the grass will not compete) If you thought you would need potash then 500 lbs/A of Murate of potash 0-0-60, would be a good idea.

It is also possible the symptoms you are seeing has little or nothing with your fertility. I would hope you have some support from the Extension Service with your questions.