Periodic 2 month Lease vs 2 year lease

Let me start out with saying I know I should probably replace the tenant however, I'm curious about my short term options.

We're 6 months in to a 2 year lease. He's paid late every month and always in 2 installments and currently I have not charged him late fees. I'm thinking about making him a deal and writting up a new lease agreement where we split up the rent into 2 payments. 60% by the 3rd or there will be late fees and 40% by the 16th or there will be late fees. Also the new lease will be a periodic lease of 2 month intervals. 

In this manner, will it give me an advantage if he defaults on lease payments because I can simply not renew basically discharging the agreement and have him out by end of lease? As a posed to him defaulting and then I have to perform eviction proceedings which is costly and probably takes longer. What do you think? Thanks for your help.