3" will be too small for the 2" squares. I think 3 1/4" is as well. I have that same drueke board and I usually use 3 1/2 or some 3 3/4" sets on it. Happy to take a few pictures if you want.
Set size for 2" square board

If you want to match a set with a board, you should be looking at the size of the King's base, not the King's height.
For a 2" square, you want the base of the King to be no larger than 1.5" (since anything much larger will seem crowded on a 2" square.

Chess Set Sizing - Pieces vs Board...
The primary sizing criteria for the set and board is that of square size vs King base diameter...
A good rule of thumb is...
King base diameter = 0.75 * square size
or equivalently....
Square size = 1.33 * King base diameter
Any variation from these ratios, or the size of individual pieces and pawns is a matter of personal preference...
http://blog.chesshouse.com/how-to-select-the-right-size-chessboard-for-pieces/

For a 2" square chess board, you want a set whose king's base diameter is 1.5".
Since you mentioned the HoS and your affinity for Reykjavik-style sets, consider the following:
- The Fischer Spassky Series Chess Pieces - 3.5" King
- LIBRARY Reykjavik Series Chess Pieces - 3.25" King
If you're a Fischer fan, The Fischer Dubrovnik Series Chess Pieces - 3.625" King would also fit but is currently out of stock.
Hi all,
I'm looking at a vintage drueke board with 2" squares. I have several sets with 3 3/4 inch kings which I have typically used on 2 1/4 inch boards, and am comfortable with this size ratio. Regardless, I'd like to buy a new set for this board. I'm hoping to evoke a feel of late-midcentury to 70s time period, with a somewhat simple aesthetic (but not German knights). Basically, I like Reykjavik-72 style sets and similar (I'm not too concerned with being a true historical reproduction).
I notice HoS has this set in the standard 3 3/4, but also a "library size" 3 inches. I'm wondering which size would be better for the Drueke board. I think overall I'd prefer the 3 3/4, but I'm concerned about overcrowding. But on the other hand, I just feel 3 inches is a bit dimunitive, I'd prefer 3 1/4 to 3 1/2.
Anyone have a board in this size and what sets do you like playing on it?