Hi sbrault74,
No, links that have been disavowed will not disappear from your GWMT most recent links list.
Google has made it clear that a disavow instruction is treated as a suggestion only and since the links have not actually been removed from the web, they will remain visible in the list.
Googler John Mueller made this clear in a public Hangout a few months ago.
While it is difficult to make judgements about your process, whether you have provided sufficient detail in your reconsideration request etc, there is one area to consider that jumps out at me from your post.
It seems the only data source you have used to identify troublesome links is the GWMT list. Google provides only a sample of backlinks in this list, and we know from experience that every tool which provides backlink data will return a different list. While there will be some overlap (which means you will need to deduplicate your list), there is always a number of links found by each which do not appear elsewhere.
You should also make sure that you include links from any old SEO reports and other lists that may have been provided by link builders etc.
There is information in these slide decks that will give you some tips (and there are some almost invisible links in the slides) for data mining and email outreach:
Move or Remove, The Where, Why and How of Dealing with Penguins & Penalties
10 Link Removal Mistakes You Never Want To Make
and if you haven't read this post from Ryan Kent yet, you should do that before going any further.
If you are looking for tools and resources that might be helpful, you will find a short list of both, including a reconsideration request checklist in the sidebar of rmoov.com under helpful tools and resources.
Hope that helps,
Sha