Messenger Plus! doesn't interfere with the connection to the Microsoft servers. Therefore the slowness of games and slow log in times must be attributed to something else.
Both could be caused by line attenuation where the line (your internet connection) is saturated.
Alas the second issue can be attributed to a larger contact list. The servers send you your contact list each time you log in. If your line is saturated the reception of the data will be slow.
There was, previously, an option to debug the connection for Windows Live Messenger. If it is available try it and see where the connection is taking awhile. (This was apart of Windows Live Messenger, not Messenger Plus!.)
On your "more private account" are there issues with games? Have you tried a mobile version like
https://meebo.com to see if you experience any slowness with the logging in?
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