A high Efficiency heating/cooling system does not necessarily translate into a higher house value; you have to find someone who appreciates what a geothermal system really is to get a good return on your investment. Most people are so focused on the price; they often forget that spending a little more will save them in the long run.  Case in point, most of what the big box stores sells (Home Depot / Lowes) is low quality for low price. My parents went through two hot water heaters in Five years they brought from Home Depot, a plumber friend said Home Depot sells stuff for the lowest price, cause most of it's crap. A well made water heater from a pumping supply house will cost more, but lasts a lot longer. 

They do make air conditioner for casement windows, they might be a little more pricey, but if you can live with only cooling a few rooms, it's might be a good alternative.

So let's run the numbers here,

Option #1 replace the entire system with a Geothermal system, I'm assuming closed loop, based on the 20 to 30k price tag. Figuring 50% rebates the system ends up costing you 15k worse case, assuming a 30k system.  (I'm assuming your state is offering you some kind of incentive, since the Federal rebate is only 30% of the cost of the system) Comparing your new system with your old, assuming Oil is $4 a gallon, and you use 300 gallons a year, the cost would be $1,200, this assumes your electric bill does not increase running the new geo system. Number of years to break even, 8.3

Option #2 Replace only the Air Source Heat Pump with a high efficiency Air Source Heat Pump. Cost 5k. You will probably see a modest savings on your electric bill, but nothing major. (Federal rebate, 30% up to $1,500) So your cost is $3,500 with rebates.

Option #3 Replace the Air Source heat Pump AND the outdated Oil system for 9k. This yields you a modest savings on your electric bill, but replacing the outdated oil furnace which range in efficiency anywhere from 56 to 70% with a new high efficiency oil system which are 90%+ efficient could save you 20% or more on your oil usage. So instead of using 300 gallons a year, you could use 240 gallons a year instead. (Federal rebate, 30% up to $1,500 for the ASHP AND up to 30% up to $1,500 on the oil system. You'll have to check with the IRS, I'm not sure if you can collect on both) So your cost here is $6,300 with rebates.

My recommendation? Ask the heating guy to check out the oil system, see it's it's at end of life. If he says it good to go for another 5 years, I'd just get the ASPH done, since your not keeping the house anyway. If worse comes to worse, you can have it changed out later. If not get the oil system done too. In my opinion, your saving isn't going to be major here by switching to a geothermal system and there no guarantee that it's going to increase the value of your house. If this was an all oil heated house where you were sucking down 1,200+ gallons a oil a year, at $4 a gallon, that's over $4,800 a year. In that situation, changing to Geo certainly makes sense.

I don't see a problem with it, if you oversized the geothermal system / heat pump, the system would cool too quickly for proper dehumification. I don't know of a  problem with heating up things too quickly. So long as your rebate offsets the additional cost of the bigger furnace, it's fine.