Suggest a basic level split system HP as you suggested, and a consider a minisplit heat pump on the addition. Using a minisplit would give added heat and be more energy efficient at AC cooling than a window unit. Also probably have a better warranty.

Obviously humidity will be a big concern with your cooling. Don't upsize thinking it will bring better cooling. Make sure it is sized correctly, so you will get a long enough run time to get good dehumidification. It's nice long run times that pulls out that humidity.

Mobile home systems are specifically sized to fit into their smaller utility closets. Mobile home furnaces are specially rated by UL. So you may be limited by what will fit.

I'm not too keen on putting a split system back in place. Not a lot to choose from that will fit the small confines of the HVAC closet. Also would like to move as much of the noise outside as I can.

My thought with the package unit is that I can remove the furnace and existing A coil and run the additional duct needed this summer and fall. In early fall I can set the unit in place and wire it in. Will run new thermostat wire at the same time I run the new duct. Trying to do as much as I can myself to make it as budget friendly as I can. Right now I am looking and Rheem and Whirlpool brand packaged units. Have had a WP package unit in the past was was impressed with how it just ran and worked well all the time.

I had not considered a Mini-Split for the addition but that sounds nice. Would be quieter than what we have now and would not block the view out the window.