There's another option. It's annoying, but cheap. Once you set your Workbench screenmode to a 31khz mode, turn on Mode Promotion in IControl or add another screenpromoter utility. That should get Workbench-based stuff working.
OS3.9 BB2 also promotes (or is supposed to promote) the early startup menu. From there you can force boot into Double modes for games, etc. I don't know how compatible it is with games (some are really troublesome with NTSC/PAL, the doubled modes might have the same problem). You'd need the VGA adaptor and you'd need to set the mode on every boot.