Solid Hardwood, Engineered and Laminate Flooring - Installing baseboard - Help!

This my first baseboard project and I’ve run into a snag. I am installing 1-piece, 5” tall, stain-finished baseboard onto an uneven sheetrock wall and am getting gapping. My current strategy is to place the baseboard against the wall and add plaster material to build up the areas where gapping occurs, and feather it up the wall a bit. Is there a better way to do this? with painted baseboard I would simply fill in the gap with paintable caulk, but I'm afraid this wouldn't like good with stained baseboard. Also, I will be securing the baseboard with a finish nailer, but am concerned that nailing at each stud point won’t securely hold the baseboard. I’ve seen toggle anchors used to secure screws in sheetrock. Are there any toggle like devices that could imbed additional securing surfaces into sheetrock…like an imbedded segment of a furring strip that a nail could go into? I’ve thought of drilling holes and gluing in large dowels, but I don’t think that would be secure enough. Any thoughts?

I would greatly appreciate any insight you could provide.

Dont know about your particulars, but I've done lots of baseboards and crowns - painted and clear. Walls in older homes are seldom straight as you can see. I just installed natural (clearcoated) base in my current home after a re-tile job. I used a brad nailer and evenly spaced dabs of construction adhesive to install. Filled the brad holes, then using blue painters tap, masked off the top edge and used white (or clear) paintable calk long the length of each piece to seal the seam (and gaps) between the wall and base. When dry, touch up with wall paint then peel the tape away. Sand and finish the base with stain/clear. Did the entire house this way and looks great.....and more than enough fastening power as they are purely decorative and on-structural. Hope this helps.

Also, where the corners meet (outside mitered, inside coped), I use Pergo calk/sealer/adhesive at the joints as the color mostly resembles natural wood and seals/holds the joint together quite well, and it makes the inevitable seam invisible.