Hmm, 2200 x 1600 pixels, 1 bit depth, sounds like you're dealing with faxes. My guess is that you're receiving fax images for viewing via http. Under that assumption, you do not want truecolor at all. If you use PNG, go with greyscale or a two color palette. You might also consider GIF (again with a minimal palette) and see which gives you smaller file sizes.

To serve fax images, I would convert the image format upon receipt without resizing it. If you can keep the bit depth down the image files should not be very large. Let your visitors' web browsers do the resizing by using the height and width attributes in the IMG tags. Your server can reset these a lot faster than it can resize the images. You could also use these attributes to have a resizing function on the client side with a small bit of javascript.

Update: Converting some TIFF fax images (avg 80k) to PNG, I get a smaller size PNG even in truecolor (avg 76k). However, by saving the PNG files uncompressed in truecolor, they are several times larger than the original TIFF (avg 460k). So my guess is that your converted files are not being compressed.

Original 2 color TIFF: 80kb

Convert to Trucolor PNG, compressed: 76kb

Convert to Trucolor PNG, uncompressed: 460kb

Convert to greyscale PNG, compressed: 58kb

Convert to 2-color PNG, compressed: 48kb