"contribution {to|toward|towards} ‹gerund phrase›" in AmE in a non-monetary sense

I would like to understand which preposition to use with "contribution" when it is used in a non-monetary sense in American English in the case when the preposition is followed by a gerund phrase. My example is:

The work of X is an important contribution to/toward/towards a better understanding of White-Zweistein manifolds.

The pages http://www.oxfordlearnersdictionaries.com/definition/english/contribution, "Contribute for" or "Contribute to" or "Contribute on" or "Contribute in" and "Toward" or "towards"? seem to be of different opinions with varying degree of explanation. Regarding AmE, I found out that "toward" sounds better that "towards", but I could not find out the relative order between

• "contribution to ‹gerund phrase›" and "contribution toward ‹gerund phrase›"

as well as the relative order between

• "contribution to ‹gerund phrase›" and "contribution towards ‹gerund phrase›"

in the non-monetary sense.

Which preposition would sound best in the above example and why?

Contribution to is more frequently used in news before a gerund than contribution toward/towards. Thus, it must be quite "better".

If you do a quick research for "contribution to " on News Search engines (Bing, DuckDuckGo, Google), and then do the same using 'toward' or 'towards' instead, you'll have the opportunity to check it for your specific case. Take a look in the amount of results each preposition have after 'contribution' with the picked gerund.

I did it with the following gerunds:

• understanding (I picked because it looks unlikely to be used in a monetary sense)
  • "contribution to understanding": 2,030 results.
  • "contribution towards understanding": 50 results.
  • "contribution toward understanding": 50 results.
• supporting (however this one might be more likely to be used in a monetary sense)
  • "contribution to supporting": 2,970 results.
  • "contribution towards supporting": 111 results.
  • "contribution toward supporting": 4 results.

I did it also with and establishing and recording (which has only 1 result for towards/toward), and got similar outcomes. Also tried variations to the verb (3rd person 'contributes'), and the results were the same.

Thus, I conclude that towards/toward are less used before a gerund in formal writing. I suggest you to do a similar research with the gerund you intend to use, anyway.

PS:

• It doesn't mean that the less used forms are 'wrong'. But the first one is even more unlikely to be a mistake, either.

• I couldn't post the links to all the search queries I did because of the 2 links per post limit.

  EDITED in Jan, 13 2017. The previous text didn't fit the asked use - the noun contribution, rather than the previously shown verb contribute. Removed the word overcrowding of the examples as it has no results in search. Added the recording gerund, instead, to come with more examples. Changed the "proportion" in my tone, as with the verb the proportion is significantly greater in favor of to. When using the noun, it's still much greater, but not as in the previous case.