I would not link the abbreviation only. The abbreviation should be placed in brackets after the first (and only) use of the full phrase which is abbreviated. The abbreviation is therefore in brackets as an advisory of the contraction and of its subsequent use in exchange for the full term. The abbreviation is not in itself the item that requires linkage, it serves a different purpose.
If you link the abbreviation and not subsequent uses of the abbreviation, the first (linked) instance of the abbreviation looses the visual relationship (font, colour, appearance) with the subsequent uses when people look back for the first use. It obscures the mechanism.
In addition, for those following content with automated readers, the abbreviation would become the focal point or node of the link and that seems incorrect, although the title text of the link could re-expand the text.
Nor would I put the links at the bottom of the page. To do so would be to extract that particular item from the content as being of importance to the whole story, and one which you may wish to follow up on for related information. That's fine if that happens to be the case but to do it because the phrase is long is inappropriate and unnecessary, misleading even.
I think you are trying to resolve a problem that does not exist. I believe the correct thing is to link the full term. It only looks odd if you have very few words in addition to the long phrase, and to say it looks ridiculous is being harsh.
I would add that appropriate link colours reduce the need to even look for a 'solution'. For example, dark blue links among black text makes the phrase stand out less, aids readability and flow. Of course it has to be distinguishable as a link, so there's not that much scope for messing around with the colours. Darkening visited links also helps.
In addition paragraph width plays an important part in not making the content look awkward. Narrow paragraphs are inherently going to have links that break lines - maybe even several lines. Neither does this require a 'solution' - I mean what do you do? Deliver content optimised for link length based on a media query that takes into account paragraph width and changes what's linked when the user flips a device for landscape to portrait. Of course not.
By way of an example: A website which has a huge amount of content and is very particular about their manual of style, Wikipedia is quite happy to link long terms or phrases without considering it a problem. For example in their article on the United Nations Educational, Scientific and Cultural Organization (UNESCO), they include a number of long links, some of which are abbreviations such as United Nations Conference on International Organization (UNCIO). Others, however, are terms which may not even have an appropriate abbreviation, such as the Convention on the Protection and Promotion of the Diversity of Cultural Expressions. To use an abbreviation purely for the sake of making a link shorter is obviously doing the wrong thing for the wrong reason.
No - the only actions that fit all situations are:
- Link the term itself, however long it is. Just link it on first use, and link it once only.
- Don't link it at all. Ask yourself, does it really add value?