Using integrated fork with non integrated headset
 

I am building up a bike out of spare parts and I have a KHS Flite 800 frame with a Modus M550 standard threadless headset. The cups are already pressed into the frame. I have a fork off a Fuji Team that is an integrated fork (I think cause I can't put any of the bottom half of the headset on it and it looks like it was meant to take bearings). The fork originally used a Ritchey Logic zero stack headset. So far I just stuck the bearings on the integrated part of the fork and stuck it up into the cup pressed into the frame. I then assembled the top part normally. Do I need to somehow remove the cups from the Modus headset and start over with a new Ritchey Logic zero stack that the fork was designed to work with or can I just use this cheap solution which seems to work but perhaps is a bad idea? Also is there anyway to use an integrated fork with a nonintegrated headset? (I want to find whoever invented the integrated headset and %^&$##) What is the cheapest integrated headset? I want the cheapest possible solution to this problem as this project bike is waay over budget. (Just to clarify right now all I have is the integrated fork with the ball bearings on it stuck up in the cups that are pressed into the frame - this doesn't seem like it will be good.) Anyone know how to remove pressed in cups? If I have to buy a new headset than this whole project is ruined cause it costs way too much and I ended up losing a ton of money.

Let me know what you guys think and thanks for any advice

Well you certainly can't use an integrated headset on that frame, the headtubes are different y'see. As far as I'm concerned, as long as the bearing on the fork fits in the cup on the frame it'll be fine (compare the bearing with the original from that headset if you still have it, most likely the standard size though, unless it's a sealed headset), but you might have issues with keeping dirt and stuff out, and it might look a bit odd. Other than that, it's new fork or new frame time I'm affraid.

I think you ought to take the whole mess to a good bike shop. Park tool has how to on headsets types installation and removal. Just as a place to start,you need a crown race on that fork