Should I 'keep' the messy tenant who will pay post renovation rent without renovation?

[John R.]

I'm in the middle of renovating a property that is C class in a nice B+ to A neighborhood.  The renovated units are renting quickly.  One guy has lived there for years and I don't think he has EVER cleaned his apartment.  Black funky mold in the shower, dust on the baseboards and door jambs.  But he pays on time and does not appear to cause any trouble.  I've had the place for about 5 months now, so don't have a long history with him.  Anyhow, he wants to stay and says he is willing to pay the higher, post renovation rent to stay in his current unit as it is.  Doesn't want to move into a renovated unit, just wants to stay put.   

I'm changing the culture of the building and so inclined to move him along, but due to the state of his unit I will probably have a higher renovation expense on that unit.  And it may be worth noting that I like my buildings nice.  We keep them well maintained and tidy with the idea that good tenants want updated, clean spaces and are willing to pay a bit extra for them.

Do I let him stay, at least another year until all the other units are turned, or does he need to move on?  Maybe the messy apartment is a flag that there will be problems later on after the lease is renewed?