Sweeten the pot with a refund of 1-2 weeks of rent if they get out faster.Whatever you do, get rid of them.

You can sweeten the pot by telling them you'll refund the deposit within 24 hours as long as there's no damage to the property, or something to that effect.

If a seller's sticking point isn't the price, you can offer other incentives like a high pure-interest rate for a shorter term or something like that to sweeten the deal.  

Would it be smart to offer a lump sum of cash every few years to sweeten the deal to persuade the seller?

Time is money, and getting into a property quickly can make the difference in getting or losing out on a deal.Being able to read realtor remarks in the MLS, run sold and rental comps more efficiently, earn commissions or waive them as part of sweetening an offer to a seller, and save on seller-side commissions while selling are other big advantages as well.

If you are able to - you may want to sweeten the deal by having the balloon payment triggered upon his death so his kids get the funds (assuming you know more about the inhertance tax implications than I do!). 

Sure, there can be investment components that sweeten the deal that are not obvious, but when you need to dig hard to find them, it’s probably a lousy investment.In those days, the herd was heading to the cliff.

To sweeten the deal you could also offer slightly more than what he is asking for.

Any other suggestions on how I can sweeten the pot?

States have different laws about the occupancy of a unit to an owner and it's a little unclear on FL - but one thing to consider is cash for keys.To ‘sweeten the pot’ (and your timeline) you can also select a favored unit and offer cash for keys in which you’re basically are saying “here’s the notice of me not renewing your lease as outlined with x amount of days notice/can we come to agreeable terms to vacate sooner” so with an agreed upon arrangement of them vacating (get in writing)- especially if lease has outlined that it will continue with transfer of ownership and not near end date.