MySQL configuration to connect to multiple local applications
Not really an answer, but too big for a comment. This is quite a specialised question and would probably (IMHO) be better off asked on the FreeRadius mailing lists.

I looked here and found this


  FreeRADIUS is a high-performance and highly configurable RADIUS
  server. It supports many database back-ends such as flat-text files,
  SQL, LDAP, Perl, Python, etc.


The problem with many systems which support multiple back-ends is that they end up not being optimised for any of them - it's possible that something in their code conflicts with MySQL's way of doing things. And I'm not even sure what a "Perl, Python, etc." back-end is - drivers? 

From here, it appears to me that the default database is PostgreSQL and it's possible that scenarios which work with PostgreSQL either don't work or work poorly with MySQL. So, my second suggestion is to try that RDBMS (which, in any case, is superior to MySQL IMHO).

[EDIT] in response to the OP's queries.

Just out of curiosity - what are the response times of those queries when run separately? Second, the issue appears to be a lock on the radacct table. This is a problem with MyISAM tables which your system uses.

Could you take a dump of your schema using mysqldump, change ENGINE=MyISAM to ENGINE=InnoDB, 

sed -i 's/ENGINE=MyISAM/ENGINE=InnoDB/g' your_schema_dump.sql

load the edited dump file and rerun the system to the point where you are having the problem? There is very little to be said these days for running a system using MyISAM tables.