Does anyone have a ball park figure of the cost to rechamber an N frame 357 to 44 special? What is involved in this.

Bowen does a great job:

+ C A T A L O G +

The rechambering should be in the neighborhood of $200 or a little less.

What is involved is using the proper sized piloted reamers to open up the chamber throat to the desired caliber, and then using the proper sized piloted chambering reamers to first rough, and then finish ream the chambers. This is best done on a milling machine with the proper fixture to index and hold the cylinder. At the very minimum, an accurate drill press with minimum runout and cylinder holding fixtures are required.

And then there is the matter of a barrel. Do you have one already or are you planning on having the .357 barrel bored out and re-rifled?

Unless you have the parts already, it will probably cheaper to find a M-24-3 or -624 already in .44 Special than to pay someone else to do the work. The sale of the .357 you already have will take you part of the way.