> is there too much hive trash in the mineral oil by the end
> of the week to make this feasible?

You are not the only one who fails to get back to a yard in a timely manner,
and is rewarded with more hive trash than mites.  :)

I'd stick with sticky boards, and not use any oil.
Just scrape the entire contents of the sticky board into a gallon-size
ziplock bag or a Tupperware container with a plastic 6-inch putty knife:

For a less messy board, pour the whole mess directly into ethanol (AKA ethyl
alcohol, " methylated spirits", or "denatured alcohol"), the mites float,
the trash sinks, count away.

For a very messy board:

1) Soak the sample in 80 % ethanol for several hours 
2) Add as good a saturated salt solution as you can make.
3) Stir gently
4) Let things settle out 
5) Count mites that float, and call that 95% of the total mites, as a tiny
number of mites will be still stuck to the trash, and/or weighted down by
the trash

> Second question, any tips on making it easier to count the mites in the
oil?

How to count?  MATLAB is your friend.  Take some high-res photos of the
floating mites using good lighting to get some contrast.

There are multiple YouTube tutorials on counting objects in images using
MATLAB. As varroa have a distinct shape, and almost never float on their
sides, the many code examples used for bacteria will work well.  If the code
leaves you stumped, I speak MATLAB.

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