You could try grinding the K2CO3 in a pestle and mortar. In my experience this leads to MUCH higher rates than the more coarse granules out of the pot.
Also, have you tried biphasic conditions? A typically way to put a carbamate on amines is to stir with the chloroformate and aqueous K2CO3. It's always surprised me that the chloroformates don't rapidly hydrolyse under these conditions, but it works. The carbonate is only there to mop up the HCl you form in the reaction (a la Schotten-Baumann).
Is there any other reason the reaction might be slow? Hindered amine? Is the amine SM a salt, and if so are you adding an extra eq. of base?