Commercial tenant default -> opportunity to strengthen lease?

[Davy Crockett]

I am the landlord of a commercial gastro space in NY State. The tenant has been regularly past due in his rental payments over the last several years but does pay the rent after an average of one month delay. That delay bring a negligible late fee calculated as an annual percentage. He is currently caught up except for one month delay. 

According the terms of the lease, he is in default such that I  COULD immediately lock the doors today and all FF&E becomes my property. I have the right, according the lease terms, to lease to a new tenant and any difference in rent is former tenant's responsibility. 

Ideally, it won't come to this. As I said, the tenant's only incentive to pay the rent on time is the worry that we kick him out. If he doesn't think we will exercise the terms of the lease (default), he doesn't worry about paying on time. 

The tenant has now indicated that he is unable to pay the rent and would like a postponment of rental payments to be covered as additional rent over future rental payments. I believe it is not a problem of cash flow but rather of poor management and lack of incentive to pay. 

Therefore, I do not want to provide this leniency. Alternatively, I would like to use the opportunity to strengthen the terms of the lease. I am considering defaulting the lease (w/o termination), locking the doors, and requiring an amend ment the terms of the lease before re-entry, such that any delinquency of rent would incur an immediate one-off penalty of a reasonably significant amount, plus a higher late fee percentage (daily compounding of annual rate). 

I am not concerned that my terms would be met due to the profitablity of the tenant's business and significant investment there in, however, I am concerned about the implications of undertaking this relatively aggressive strategy including any legal implecations to to which I may be bound according to NY State law (Usery laws..? ) . 

Although finding an amicable solution would be generally preferred, especially since legal fees would likely be incurred based on this strategy, I am fed up with this tenant and therefore am considering the above. 

I am grateful for any suggestions or thoughts any of you may have and wish you a happy Easter, should you celebrate it.

Davy