Merging multiple log files by date including multilines

I have several logs containing lines all starting with a timestamp, so that the following works as expected to merge them:

cat myLog1.txt myLog2.txt | sort -n > combined.txt

Problem is, that myLog2.txt can also contain lines without a timestamp (e.g. java stack traces). Is there an easy way without any custom scripts to still merge them and preserve the multiline content?

Example myLog1.txt

11:48:18.825 [main] INFO  org.hibernate.cfg.Environment - HHH000206: hibernate.properties not found
11:48:55.784 [main] INFO  o.h.tool.hbm2ddl.SchemaUpdate - HHH000396: Updating schema

Example myLog2.txt

11:48:35.377 [qtp1484319352-19] ERROR c.w.b.c.ControllerErrorHandler -
org.springframework.beans.TypeMismatchException: Failed to convert value of type   'java.lang.String' to required type 'org.joda.time.LocalDate'; nested exception is    org.springframework.core.convert.ConversionFailedException: Failed to convert from type     java.lang.String to type @org.springframework.web.bind.annotation.RequestParam   @org.springframework.format.annotation.DateTimeFormat org.joda.time.LocalDate for value    '[2013-03-26]'; nested exception is java.lang.IllegalArgumentException: Invalid format: "    [2013-03-26]"
    at org.springframework.beans.TypeConverterSupport.doConvert(TypeConverterSupport.java:68) ~[spring-beans-3.2.1.RELEASE.jar:3.2.1.RELEASE]
at org.springframework.beans.TypeConverterSupport.convertIfNecessary(TypeConverterSupport.java:45) ~[spring-beans-3.2.1.RELEASE.jar:3.2.1.RELEASE]
at org.springframework.validation.DataBinder.convertIfNecessary(DataBinder.java:595) ~[spring-context-3.2.1.RELEASE.jar:3.2.1.RELEASE]
at org.springframework.web.method.annotation.AbstractNamedValueMethodArgumentResolver.resolveArgument(AbstractNamedValueMethodArgumentResolver.java:98) ~[spring-web-3.2.1.RELEASE.jar:3.2.1.RELEASE]
at org.springframework.web.method.sup