RE: What plane could this be?
I don't think it's a Conquest IV. I have a Phillips Conquest IV and it doesn't match up with your plane very well at all...
My vote would be: maybe a fiberglass knock off of the MK Cosmos, possibly made by Phillips Aircraft...I wouldn't necessarily call it a perfect match but it's about the closest thing I can think of. Maybe seeing some pictures of the vertical, wing and stab cores may help narrow it down??
The first photo below (pink airplane) is a Conquest IV...The other three pictures are of the MK Cosmos for comparison.