Hi Scott,
I think Iolite is the right fit based on your optical and physical properties. In particular the fact the you have a trichroic/dichroic mineral matches the Iolite. Being trichroic - you will have THREE refractive indices. A polariscope may help confirm - Iolite is biaxial although it can be positive or negative.
But the geochemical information is totally anomalous with that. SEM uses EDS detectors (energy dispersive spectrum). These measure X-rays using silicon detectors and provide semi-quantitiative results if used with standards and calibration, which they usually are not. So they give a quick and dirty idea of what might be in the sample. XRF also measures X-Rays but will do so using a crystal detector and this measures X-Ray wavelength. XRF is more sensitive and accurate. SEM-EDS can also give a map by element - so you would be able to discriminate spatially whether you are dealing the the veil in the gem or the gem itself.
Both XRF and SEM-EDS will have problems with the lower elements in the periodic table. Anything with atomic number 11 (Na or sodium) or lower. They will analyse the skin of the material and the depth of the x-ray generation will be voltage dependent.
Iolite (cordierite) is Mg2Al4Si5O18. Mg and Al should have been detectable by the SEM-EDS and XRF - but they are light elements with atomic weight 12 and 13. So I’d be asking the question were Mg and Al detectable by the machines that were used.
The strontium (Sr) and zirconium analysis via XRF does not make sense. Strontium minerals could be Celestine SrSO4 (too soft @ 3.5 and too heavy @ SG 3.97) or Strontianite SrCO3 (too soft @ 3.5-4 and too heavy @ SG 3.785) and neither are pleochroic. Piemontite can have some strontium substituting for calcium which is plechroic but from red to yellow. It is part of the epidote group of minerals as is zoisite and clinzoisite (think tanzanite). Tanzanite does not contain Sr nor Zr.
There is really nothing mineralogical with Sr and Zr together. If you have a zircon (ZrO2) inclusion it will be a grain - a euhedral or well shaped crystal with high relief - it will be visible. Definitely not a veil.
If you want to pursue further analysis could I recommend that you use either EPMA (electron microprobe) or LA-ICP-MS (laser ablation mass spectrometry). EPMA will require a conductive coating of carbon or gold (can be cleaned off) and will be non-sacrificial. LA-ICP-MS is sacrificial and will drill a small pit by laser (about 30 microns cubed). Discuss the mineralogical possibilities and the analyst will advise accordingly.
I wonder if your XRF results are from something else - mistakes do happen.