We use a couple, Equi Analytical is good one. Unless you have purchased hay for 6 months feeding, having the hay analyzed will be expensive and may not be of value.
I understand your concern with Se, however issues with Se content that would raise a red flag are not evident based on your comments. Most feedstuffs contain 0.01 – 0.06 ppm Se; alkaline soils tend to have higher Se levels. A horse’s requirement is estimated at 0.1 ppm for the total ration but that is considered the minimum amount to prevent deficiencies. Most commercial balanced formulas, which are a small portion of the total diet, are at 0.3 – 0.5 ppm to compensate for the Se levels in forages that are less than the 0.1 ppm minimum requirement. You can view the Se levels for each Integrity product on the Integrity brochure.
If I can help you navigate through what to feed let me know.