Hi Mark,
Go to Parameter Groups, Create a Parameter Group. You can edit parameters (MySQL Variables) as needed. Then on the instance itself, select Modify Instance to select your new DB Parameter group as the option. Then reboot the instance and confirm things. Two things to consider... (1) max_allowed_packets must be set to >16mb or AwareIM will barf. I use 128MB. If you need more than 16MB your app will let you know. (2) Check the settings for lower_case_table_names. In my case, MySQL defaulted to yes on my production db server but on RDS the default seems to be No. Make them match.
As far as I know, you don't ever get root priv's, but the above should give you all you need.