Hi Elena,

Your plan for raised beds filled with fresh soil is a good one. For children, you want to have bare soil covered.

If you do those two things, you should not have to do the sulfur remediation. The Wisconsin extension page says this about the technique. Note the boldfaced text:

"This method of amending your soil
will not make it hazard-free but
should reduce human exposure to
soil lead if any soil is accidentally
ingested or inhaled. Recommended
gardening precautions should still
be followed. Use this method only for
your garden, not for your entire yard.
Applying this amount of phosphorus
to your yard may contribute to water
quality problems and is prohibited
by Wisconsin Department of Natural
Resources regulations."

Minnesota prohibits use of lawn fertilizers with phosphorus because of worry about runoff that affects water quality. The Wisconsin recommendations are only for gardens and since you're building raised beds, you don't need to do this. 

This state of Minnesota page has helpful information:

https://www.health.state.mn.us/communities/environment/lead/home/worksoil.html

I hope this helps. Good luck with your raised beds.