The tire size wont affect the brake reach, just the rim. In fact you will gain about 1 cm of tire clearance on your frame when you go to 700c. You will need long reach calipers. I'd be surprised if your new tiagra brake calipers reach as they are mostly short reach brakes. You can get a brake bridge extender which will drop your brakes about a cm closer to the tire. Can't remember what they are called exactly so having an issue finding them for you. They are basically a piece that fits in the brake bridge and fork crown that have a new hole dropped lower down where you can attach your calipers. Don't give up on your conversion, anything is possible.