If you scour the web there are a couple articles that discuss the various ICP testing companies. I'm biased and use ATI. I've read some good things about Triton but never used them. The key to ATI's speed is to get it in before they do their weekly shipments from the US to Germany. They do two a week I believe. My last one I must have snuck it in just in time because my results came back within a week.
I do anywhere from 2 to 3 ICP tests a year and use the results more or less as a third party source to compare to my results. I run a trident. So the way I do this is to pull the ICP water samples just before the noon tests of the trident. So about 11:55 I fill the test tubes, then grab a cup of water, and last tube I fill with RO water and note the date, time.
While the Trident is running its tests I'll run a manual test of ALK and Phosphate using my Hanna checkers. Note those results to Apex. Now I have manual tests, Trident tests, and test tubes filled and sent to ATI all within 20 minutes of one another. Once results come back I can do a quick check and compare. So far everything is pretty much spot on.
And ATI does test phosphate. I don't know how they calculate it but you can probably check their site for details. Example:
Value Calculated Difference. Difference
Nitrate 0.01 mg/l 2.00 mg/l -1.99 mg/l
Phosphorus 27.00 µg/l 14.70 µg/l +12.30 µg/l
Phosphate 0.08 mg/l 0.04 mg/l +0.04 mg/l
Edit: Format messed up - sorry. You can see the values for Nitrate, Phosphate, calculated difference / reference, then result differences.