As far as this librarian can determine, though home soil tests are available (see this OSHA report), it is difficult to figure out which ones/methods will provide definitive and reliable results for the average citizen. In addition, residents who wish to test in order to take action: remediate soil conditions or pursue legal avenues may wish to undertake testing that is certified.
So, as you mention, the first place to recommend low cost soil testing for lead, heavy metals, etc. is your local university agricultural extension office: LA soil testing Where basic tests can be performed for about $7 (however, there appears to be an additional charge for metals testing).
However, if the local extension service is overloaded, you may be able to send samples to other state extension offices for testing and advice. For example: Cornell will do soil testing with out of state samples, again for fairly low cost.