Speaking of better minds, Don't see why a 309 wouldn't do the trick either.

TJ is right. Why overthink this when the 219/309 fillers are the recommended choices?
If for some reason you wish to get more 'sophisticated' or 'specific' with a choice you should acquire high temp data sheets for the BM and WM's to compare. Consult the manufacturers and engineer the thing.
Of course, getting data sheets even for the recommended choices and understanding your materials is still a good idea.

The first thing is that you need engineering to disposition the fact that you violated your WPS.
Then you need to develope a new WPS if found acceptable or cut out the 625 if not.
And this depends upon what code you are working to. Some codes make prior WPS development explicit (for example ASME Section III), some do not(for example B31.3). If there are interpretations to the contrary I am not aware of them.
The second thing is, depending upon the EXACT service intended 625 could well be quite adequate, as indicated to some extent by the properties listed above. The manufacturers would be glad to supply you with more detailed info on 625 pertaining to high temp strength, ductility, creep, etc. which should be then used by engineering to disposition the mistake.
My opinion is, if we are talking about one, or a couple welds, I'd cut em out. If alot of welds, I'd try going the other way.
As always, there is no escaping the engineering. There are no cookie cutter methods to resolve such situations, unless of course you have no concern for economics. And this is seldom the case with any of us.