There are a few ways for you to resolve this problem:
You could change the JCL for Solve so that the LOG DD statements are not directing the output to SYSOUT, but to a dataset instead. Some sites use a GDG definition to manage such datasets. Typical DCB parameter values for the LOG datasets are:
RECFM=VBA, LRECL=137, BLKSIZE=15476, DSORG=PS.
The allocation is usually done in cylinders with a primary of 10 and a secondary of five, but you would need to experiment with the allocation to see what works for your site.
Other than that, the next couple of options would involve the System Software team:
Remove the OUTLIM statement from the JES3 MAIN statement.
Put an Exit in place that allows you to specify certain jobs which can go beyond this self-imposed limit. Without such an Exit the system will abend any job that reaches this limit, no exceptions, this is the Operating System default action.
By reducing the number of certain messages that go to the log all we are doing is extending the time the region has before it eventually reaches the limit. You need to discuss your SOLVE Logging requirements with your System Software Sysprogs and highlight the implications of the overall strategy upon SOLVE.