You can rent a hot water spray/vacuum and get a lot done yourself but ask the landlord or property manager.

The other unit smells heavily of Kilz spray which has been used to cover up previous pet odors, but I'm hoping this can be ventilated.About the owner: He is 74 yrs old, wanting to retire...

Also you told us you had the apt upstairs sprayed for bugs.

@Holly ScottOne option is to spray foam the floor under the floor with 4" minimum (~R-24).  

Nice,He could have just used 2 cans if spray at dusk with a rake and been all done.

Should I get a spray on?  

Look into your local codes for tread depth minimum, you may be to narrow if you take the bullnose off.Just looking at a quick snapshot of your picture there are a couple ways you can achieve a desired result.Using the vinyl: clean the leading edge of the lip up, rip a piece of the planking, using a spray 90 adhere the ripped piece of flooring the the leading edge and then glue the tread planks to the tread.I don't know how the edge will wear but that is one way.You could also do the same thing then finish it with an aluminum nosing, this nosing will assure an edge that will last a long time.They also make a rubber nosing that will do the same thing as the aluminum with a different look.You can easily source any of these on line.

We just spray painted cabinets, and the tenants love them.  

The neighborhood drug dealers were angry and destroying parts of the building; pulling down the fence, breaking the gate and front door and spraying graffiti everywhere.

Now I do it...I spray the outdoor units with a hose mounted soap (my guy just uses water) I get it at the hvac store, spray around the units with incecticide to keep fire ants out, change the air handler filter and drop off a supply of filters.