This answer might not adhere exactly or fully to the question's demands, yet I believe it contains some valuable information. Here several sources to collect idiomatic expressions or collocation are presented. (*) The expressions in italics in this answer were confirmed (and several were discovered [previously unknown to me]), using the tool in point 2.
1. Lewis and Short dictionary
naïvely as this may sound, L&S is the best source I was able to find for the seeker of Latin idioms. Indeed, each entry in L&S contains wide range of meanings and usages - especially if they are idiomatic in nature or less trivial. Thus under lingua you will find fave lingua, and under pes you will encounter the given example of "nec pedes nec caput" (several times) along with sub pedibus and others. Even proverbs find their place in L&S: in litus we will meet with "litus arare" and "in litus harenas fundere"; my reason says (maybe wrongly) that if proverbs are to be found in L&S, eo magis (all the more so) are idioms. I'll venture to say, and I mean that quite literally, that if one can think of idiomatic expressions yet can't find them in L&S, I would like to know them (this might help us to refine the search, and find another great source).
The industrious seeker might also take a look at Forcellini dictionary(digital online!), sometimes it may have phrases or quasi-idioms or collocations that L&S does not seem to give much space for. The collocation praebere usum, for example, which is pretty ubiquitous, is quite hidden in L&S, but finds it's place in Forcellini.
2. Latin Collocations Tool
This very question was a source of inspiration for me; when I read it, about a year ago, mihi in mentem venit (I thought of) making a tool for locating Latin collocations; it was ante oculos (in my mind) during all that time, so I was laetus et alacer (enthusiastic) to finally start working on it recently.
This tool by itself has no pretense whatsoever to do anything else rather than to find the technical/mathematical collocations (for that reason it has value of it's own, and stands in it's own right). Yet with common-sense and effort, the user may use it for various ends; one of them is to find idiomatic expressions and collocations - as demonstrated by the phrases in italics scattered in this answer. Using this Tool I was able to learn several new idioms like "rumpe moras!"(#5) or "osculum figere"(#2) [they are idioms in the sense that unless one encounters them, the chances for him to use them "naturally" are quite low]. Many other expressions one expects to find are there, like: bene rem gerere, mos gerere, immo pectore, niti genu, videre ut and many more.
Those phrases above you can usually find in L&S (just to give that dictionary yet more credit), but this Collocation Tool does provide some additional information, especially with respect to collocations and language usage, that is hard to obtain from L&S. It might be advisable to use this Tool, also, for one who wonders what is the more usual adjective(s) to describe "mad dog"(rabidus/rabiosus), or by what words we ought to express "strong smell": the Tool suggests "gravis" is the more natural choice, but also hints that the somewhat-surprising "taeter" might be used (probably in cases where the smell is intolerable). [yes, L&S has them both under odor]. But also, the Tool might readily answer questions like: Which verb for drinking is least related to alcohol? (indeed suggests "bibo" and "poto" both strongly usable) or Which verb do insects fly with? (suggests(#15) "volo" is valid).
3. Latin phrase-book by C. Meissner
This book is a wonderful collection of Latin phrases divided by subjects. Many of the above idioms and collocation are to be found there, along with others like sua sponte; The expressions to be found there are sine dubio (clearly) abundant in the mouth of him that has an excellent command of the language.
4. Other sources
The following sources are to be mentioned together and separated from the above since they are too far from the question's demand, and has several parallels. Yet they might turn out to be useful, each in his own unique way, and for this reason they are presented here:
With respect to English-Latin direction, mea sententia (I think) this Dictionary of Latin Phrases, is great source. It offers several ways to express the same thing in Latin - thus, it is almost bound to meet idiomatic phrases. Under "it will never be/happen" many options are presented: proverbs like "ad Graecas calendas", "cum mula pepererit", but also more idiomatic expressions like usu veniet.
In a comment @tom-cotton suggested "Latin Proverbs & Quotations" by Alfred Henderson, that was already proved to be useful for the OP.
Thesaurus Ellipsium Latinarum is a neat dictionary and enjoyable to skim. For many entries it gives some immediate collocations in a handy format: with in (many times with numbers and a new-line). Apart from its simplicity, what I like about this dictionary is that it contains examples where the entry lemma is only implicit. Thus, under colloquor, we can find solus te solum volo where the colloqui is implicit. It is basically idiomatic way of speaking. Thus under negotia we find millia curarum.
This online Latin Dictionary contains what he refers to as "Locutions, idioms and examples", but it seems difficult to glean the expressions from there (which, indeed, many times are there).