I expect that Skyline is handling this as we would expect, give the RegEx already in place to extract this value:
private static readonly Regex REGEX_IRT = new Regex(@" iRT=([^ ,]+)");
However, Skyline is still likely waiting for you to define which peptides are your standards and what standard iRT values you want to use. I am sure we could make this better, but I think all you need to do is define a new iRT library in the Peptide Settings - Prediction tab (click the button with the calculator on it), choose your standards from the available list and then click the Add button and choose "Add Spectral Library". Then point Skyline to the library for your .msp file. This should allow Skyline to import and calibrate all of your iRT values to the standard.
I am sure we could improve this workflow to auto-detect the standard in your library from our existing list, as we have been doing in other cases recently. But, for now, this extra step is required. Hopefully, you find it easier than your conversion script.
Thanks for sharing your experience with a downloaded Prosit .msp file. Have you tried building your Prosit libraries directly in Skyline? That should really be the most straightforward way of achieving your desired end-result.