I may be the queen of stickyboarding as I pull a 72-hour count on every colony 52 weeks of the year. (Barring the odd week or two when severe weather, or in my case the 'flu, has kept me away from my yard.)

I use cut-to-measure sheets  (i.e., not the standard size offered by bee suppliers ) of Cor-o-plast as the substrate with a generous swipe of any kind of too-old-for-the-kitchen cooking oil mopped on with a paper towel. Oil lives in one of those hot dog stand condiment squeeze bottles with a narrow spout.

I use double bottom boards: a screen bottom board on top of solid board so the Cor-o-plast surface is contained within the sealed-up bottom board. Sealed up with various closures depending on the season.  Right now in frigid upstate NY, the back slot has a plug made of vinyl-foam air conditioner weatherstripping, covered over with 3-M Original Blue Painters tape, with mouse-proof screening stapled over the area.  During the the winter the front is the active observation slot (bees are rarely being pests when I'm pulling boards in the winter)and it  has a custom-made wooden closure, and is further sealed with more painter's tape. The wooden closures are simply furring strips, hacksawed off and sanded down to fit.  (I obviously have no carpentry skills.)  In the summer the solid bottom board is turned around so the sticky board slot faces the rear to make doing checks easier, even at night. My equipment is all standard Betterbee and I estimate the height of bottom board to be about 2.5".

My routine is this: Pull board, count mites, write number on a piece of wide tape on my arm.  Then scrape the board using a flexible tool from the paint aisle that is used for doing edging, similar to a sheetrock mud-smoothing tool. (I can a find a link to one, if needed.) It cleans the board in just a pass or two.  If the board has been in long use it builds up a nice tacky layer of oxidized fats so I don't always need to re-oil. Re insert board and move down the line.  Takes about a minute per hive.

In the winter I scrape the debris on to ground but never do so in the spring or summer - scrapings go straight into a tightly sealed garbage can to avoid letting any SHB larvae find their way to pupation.

The number of mites in all but the most infected colonies in 72 hours is easily countable by eye.  And there'susually  not enough debris to interfere with the count. For really bad hives I take the board inside and using a lighted magnifier (the kind often used for grafting) to pick up each mite with a slightly chewed and moist wooden toothpick and set it in a cleanish spot on the board.  When I can find no more, then I arrange them groups of ten and make a count.

Bonus tip: Make a hole in the center of one of the short ends of the board, about 1/4 inch in. Install a large paperclip through the hole so you have a convenient tab for pulling it out.

Whether this method would have enough accuracy for Randy's migration project purposes, I can't say.   But it works, it's easy (and except for extra cost of two bottom boards per colony) it's cheap and accessible to any beekeeper.

I have a long-term interest in studying the debris as I think it offers many valuable clues as to what's going upstairs. For instance, once I catch the unmistakable glint of fresh wax flakes fallen on the board in early February I know the bees are busy capping brood, which means I have a laying queen (or I suppose, laying workers). That's at least month before anyone in this area would dare open a hive to check on this.  While many local beekeepers are wondering if their hive has survived queenright, I know my girls are back on the job.

Nancy

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