I've built up the stack upside down. The back of the frame sits on the counter, felt side up. Place sensitized paper. Place negative. Place glass (carefully). Drop frame around all and flip over. Use your finger tips to hold some pressure during the flip or things will shift. Then lock it down and go make the exposure.

The base on mine happens to sit quite level and sturdy when upside down. However you could easily glue down some blocks or stack up matboard or something to make a cradle.