Re: Trapping (indoor) cats
What type of room are they in?
Is there furniture for them to hide in/behind/under and become inaccessible to you?
When I trap ferals to tame/socialize, I always place them in a cleaned and kitty-proofed bathroom with one 'safe cave' for them to retreat to and hide. Chasing and blankets was a really bad idea, as you can see with the results you got, though I understand the need for having to get certain things done before your big move. Right now, you've got to do what you've got to do and there will be time for slow finesse later on.
I would recommend a cat-trap, or feed them inside cat carriers and if they let you approach the carriers you can then just close them into the carrier as they eat. Always use towels in the bottom of carriers to absorb any cat-accidents that may occur during transportation. We moved 7 cats across country, from the West Coast to Georgia in 2001 and they did great. However, if yours are still 'iffy' about human contact, I would recommend transporting them in a large dog crate so they cannot escape and have access to food/water, litterbox and enclosed cubbyholes to hide/sleep. Draping towels, blankets or sheets over these traps, carriers and crates can also help calm them down. Do not *ever* open the door to their crate unless they are in a completely enclosed place where they cannot accidentally escape or become inaccessible to you by hiding behind/in things.
With only three weeks until go-date, I would begin a very aggressive socializing program to get them as accepting of being handled as I could within that time-frame. Canned food and sitting next to them while they eat, petting. Slowly working towards more and more handling. For getting them into carriers, having the carriers prepped and ready-to-go is crucial and if they let you pet them, simply pet-pet-pet and then gently/firmly scruff and place in the carrier. I would try to do the most nervous kitty first.
Wish I lived close enough to personally help you. I'm not all that far from Atlanta, but any driving away from home more than 25mi is a bit much for me, these days.