Subject: Are there any strong, yet thin magnets?

To any bright engineer:

I am working on a stop-motion animation project that requires strong 
magnets.  The floor of the miniature set is metal.  Because the 
models are only 4 inches tall, they move out of place when I'm adjusting 
their limbs for each frame.  This creates a continuity problem.  I've 
purchased magnet sheets, cut foot shapes out of the magnetic sheets and 
stuck them to the models' feet... but the magnetic pull is too weak.  Things 
would work if I had stronger magnets.  The magnets can't be very thick, 
though, due to the fact that the models will be too tall.

QUESTION:  Are there companies that make THIN & STRONG magnetic sheets?  I 
can make the foot shaped cuts with a scroll saw if sheets are not available.  
After reading your reply to a letter about magnets, I thought you might be 
of assistance.  Any suggestions you might have regarding this matter would 
be very helpful. I'm at a stand still right now... meaning that I've built 
the set and everything's ready but the magnetic feet on the models.  I 
didn't expect this.  Tis very frustrating.

Re: Are there any strong, yet thin magnets?