Your question can be broken into 3 parts (category depth and linkjuice distribution being closely related):
1. Max links on homepage (or any page for that matter)
It used to be said to keep it under some magical threshold (60, 80, 100, etc.), but I have researched this topic extensively and there are many people who believe the number of links is not important so long as your navigation makes sense. Since 'mega-menu' madness set in a couple years ago, I struggle to see how having 200 links on your homepage can do anything other than dilute the linkjuice and domain specificity. The idea of there being a penalty or that the bottom 'x' links are not crawled doesn't carry much weight these days.
2. Linkjuice distribution strategy
I break my strategies into 2 major approaches with the difference being the method for accomplishing link distribution.
The first approach being large sites with hundreds of categories. In this case, it is better to organize logically and then use robots.txt to control (limit) the amount of internal links pointing to your less important category pages. There are many ways to do this and I'll give you an example of one way to 'automate' it. One mega menu could be used on the homepage that points to your important categories, blocking crawling for the others. A copy of this menu that allows all links to be followed can be used on second and third level categories, so the less important categories can be indexed, yet not carry the weight of a link from the homepage. This is a over-simplified example, but you should be able to extrapolate the gist here.
The second approach, for smaller sites, is to follow UI guidelines, where the hierarchy is set without regard of category value. Then, tweak your textual links to direct linkjuice to more important categories. Again, just a simple example.
3. Category depth
You've already done your research.. users don't like to click through. However, this is the natural state of humanity, so I'd focus less on how deep you ago and concentrate on the 'user experience', where your content has more sensible categorization and more relevant connections between products-categories. Do you want to be forced into click 7 times to reach the product you're looking for? (of course not) So, why not make navigating to the 'deeper' products more accessible via technology (menus, parametric filters, etc) or content grouping?