Yes, the pickups should just drop in, so it sounds like the holes are just a bit too small at the moment.
When enlarging them, you don't need to be too precise. The pickup rings will give you the maximum hole dimensions - you need to leave enough wood in the 4 corners so that you can screw the ring down firmly without the screw-holes being too close to the edge of the wood. You also don't want to extend the two cut-outs for the pickup lugs any further than the inside edge of the pickup rings, so removing the pickups from the rings and just using the rings on the top should allow you to draw lightly round the inside with a thin pencil.
Probably best if you can clamp the neck on to the body, then using a straight edge along the sides of the neck, draw some extensions of the neck line across the body up to the bridge pickup area. You can then draw a centreline between the two outer lines and use that as the basis for positioning the pickup rings. Hopefully the centre line should run through the centre of the pickup routs, but if the routs are slightly off, it's best to go with the drawn centreline and extend the routs at one end only in order to get the pickups sitting in the middle.
A small drum sander attachment on a Dremel-style tool is a quick way to do any hole extending work, though you can do it with a small file and sandpaper if you don't gave a Dremel.
As FW says, pictures help (note maximum picture size is 1500 pixels on the longest edge, so you'll probably need to reduce the pixel size of any photos you take with a photo editor - you can find free apps to do this if necessary).
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