Jitai actually has a measure in place to check that all characters in the word exist within the font – it’s lines 106 through 131 in the script. This has worked perfectly fine until just recently, but judging by your reports, it’s somehow broken! I suspect this might be down to recent browser updates that broke the approach used: especially Google Chrome breaks compatibility all the time. It may even work just fine in, say, Firefox.
I unfortunately won’t have time to debug and fix this anytime soon, but if anyone would like to fork and fix it on GitHub, I’d be happy to merge the fix in!