It is really easy to clear waivers during the free agent signing period. It may impossible to not clear waivers during this period. I had two players on waivers during this period -- one was a "Cy Young contender" making $300,000, and the other was a 5 blue star reliever also making $300,000. They both cleared waivers with no problems.
Another thing -- I'm not sure how it works in MLB but shouldn't a player taken off the 40 man roster have to clear irrevokable waivers even if the have already cleared waivers before? I thought that this was required to remove someone from the 40 man roster. Currently you can remove any one from the 40 man roster (assuming they accept the demotion -- it if they have the right to refuse) so long as they have already cleared waivers. So theoretically you could place everyone on you team on waivers during the FA signing period (which as near as I can tell they would clear with ease), and then take them off the 40 man roster, or demote them from the 25 man roster anytime later in the season with no chance of losing them.
Just my