I would treat umpteenth as a morphologically complex word having four morphemes, ump, teen, th and umpteenth itself as a whole. Adding the meaning of each morpheme does not create the same idea. Something similar I’ve seen occurs with the word cranberry. You can separate out cran and berry yet cran has no meaning by itself while berry does. Cran would then be treated as a bound morpheme in the same way that ump is as neither means anything but a vague something-like when added to certain free morphemes. I think the main issue is whether you can take ump out and still call it a morpheme even though it’s not in any other word which uses it in this way. Having a ‘vague something-like’ quality may be enough as there are many other words which also do this, due to the efforts of the mass media. I was watching a fake news show (the Daily Show) and there was a segment discussing the Cookie Monster being a bad nutritional role model for children. Stephen Colbert couldn’t get an interview with Mr. Monster and announced that he had recreated his attempt with an ‘imaginactment’ and thus cutting to him chasing down a car containing something blue and fuzzy. The entire word is nothing but bound morphemes which only contain meaning when together. There may be few examples of ump used this way but there are many words which are put together and still understood in an entertaining play on the English language.
I find this type of coinage to be deliciously satisfying.