Record DVI Signal (SXGA)
It sounds like what you need is a better DVI scaler.  A good scaler should resize your video in-line to a supported resolution for your AJA IO HD.  One example I found of the kind of thing you are looking for is here.  I have no direct experience with that particular scaler, so double check that it will handle your exact needs, but the correct type of scaler will handle resizing your video feed to something that the AJA IO should be able to handle.

Also keep in mind if you are using DVI-A (analog) or DVI-D (digital) as it will impact both cost and quality of the scalers that are available as well as the type of input you use on the AJA IO.  I'd lean towards trying to keep a digital workflow, if you can, as it should preserve the highest overall quality.

As far as alternate capture devices, two of the main ones I normally consider (though I have no direct experience with the current generation) are the Black Magic Intensity and the Matrox MXO2.  I used to use Matrox capture stuff back in the day with great success, but have not used their newest stuff.