Are you sure you can't just run on it low? Might be worth a test (late at night or first thing in the morning when coldest) to see how it runs now, and if it really does short cycle. If it ain't broke...
Otherwise, you could always pick up a smaller portable heater for when you don't need that...
Nice one on the insulation - the AC's may keep the room cool without it, but they'll be using a ton of extra energy to do so. Would be fantastic if you could record the cooling effort required before and after installation!
Without putting in a ton of work I'd agree a portable unit or just a really strong fan would be your best bet.
Bear in mind that with any kind of cooler is going to bump up your electric bills, and then most of that cool air will get lost due to lack of insulation.
Unless you're willing to put...
Just to chime in and say I'm with everyone else here. 'Free' basically means 'Hidden motive that we're going to try and pull one over on you!'
If you're happy with your system, you don't need free stuff. If you're unhappy with it, seek out some quality (and appropriately priced) contractors :)