I have been working on this for a bit. Please let me know if you find any mistakes.
Your notations of Java versions for PE is not correct. The only version of PE that ties to an update package of a Java version is for the PE 1.0, where a specific range of update versions were required due to a specific bug.
Also, regarding linking a Java version to a TMS version is invalid, as TMS does not use Java on the server side. PE uses server side Java. TMS does not.
TMS 15.2 should be removed, as that is an unsupported/deprecated version.
Also, the notation of the update package for Java in the TMSPE install guide is for reference for the version/update installed when product testing/QA was done. Except for Java6u33 for PE 1.0, the specific update package should not be taken as the only "supported version".
Another thought the on the spreadsheet as a whole, its not really a list of supported features and functions, as (for example) for all of the various devices and such, you would need comprehensive lists of actual supported TMS features (phone books, cdr's, device provisioning/configuration etc.
I am not sure what you are asking, the document I posted is just a quick reference for front line helpdesks to use when they get questioned about TMS upgrades.
Said another way, "do you" know of any training videos that show you how to configure the technology that you wrote the reference procedures for? Thanks. Jay