Update:
Mar 16th: This is when my application is listed on the website as 'received.'
Sometime at the beginning of april: This is when it actually appeared on the website.
Apr 22nd: Called in, spoke to a nice lady who said that in the last few days, it had gone into 'ready for references.' She said they're a month backlogged on actually making the calls, so have them call in. This is day 37 after the RCMP received it.