Dear John,

Well the priest would have to have a pretty darn good pastoral reason 
for walking up and down the aisle for the homily, and quite honestly I 
can't think of one at all.

Here's what the GIRM says:

136. The priest, standing at the chair or at the ambo itself or, when 
appropriate, in another suitable place, gives the homily.

Key word here is "standing".  I think language this clear does NOT 
allow for any personal interpretation on the part of the priest to 
justify walking around.

Please, when it's possible feel free to talk it over with him, but 
just make sure that the point of the conversation is your concern that 
it would be easier for YOU to understand him if he took a more.... 
traditional approach to public speaking.  :-)  rather than simply 
quoting the GIRM.

Mr. Slavek