Kriste,
Last year I planted up 4 inch pots put them in trays and slid them into one of the those clear under the bed bags(Bought at Dollarama) with holes poked into the top. I had read where someone else had done it successfully.
Well, I was skeptical it would work but it did.I had lot of plants growing. I lost a bunch when it forgot to uncover them on a warm sunny day and some of my babies fried:( I will be more diligent this year!!! You could do something similar with your lined containers.
Wendy

I would use newspaper pots inside those boxes, each box wrapped in transparent plastic and secured with some elastic band or duct tape, of course punch some holes on top of the plastic for aeration. Anyway, I would try a few things whatever is around the house before I would buy anything else.

Here is a link that might be useful: How to make newspaper seed-starter posts - video

You could also line them with coffee filters, rather than landscape fabric---you can pick them up very cheaply at a dollar store, and you wouldn't have to cut them either. I use coffee filters a lot to hold the soil from coming out the bottom of my pots. by the time you are ready to plant out, the filters will probably have deteriorated, but who cares by then? :)
gg

I was thinking of using those greenhouse nursery carrying trays with all the holes for winter sowing. Was wondering how I'd keep the dirt from coming out but I'll run with Mariana's newspaper pots and line the bottom with them.