Here is another way to possibly look at it.
What software are you using on the SE/30 to make these AIFFs? Much software from the 7.1 era needed, at a minimum, a type code attached to it. Some required both type and creator code. This is why if you use, say, Word 4.0, and you have a document from a PC copy of 4.0 with ".doc" at the end of it, it won't open it without some hassle. The SE/30 software may be programmed to only accept files with an AIFF type code, and will not accept .aif file name endings.
What you could try and do is open your AIFF file in ResEdit, and add the AIFF type code, and see if that works. If not, open an AIFF that does work on your SE/30 with that program in ResEdit, find out what it's type/creator codes are, and assign those to the file that you got back from your OS X machine. As long as the file hasn't been corrupted, I'd give it a 99.9% chance that that will work.
That is why you eventually had Macintosh Easy Open, MacLink Plus and such to translate these documents without type codes.