P2tog tbl
This block uses a p2tog tbl (purl 2 together through the back loop) decrease. If this stitch is new for you this video demonstrates the technique:
P2TOG TBL VIDEO

I have the wrong number of stitches after working row 3—why?

When working yarn overs (YO) between a purl and knit transition pay special attention to the number of stitches you are creating. The row starts with K3 (the garter edge) and then P2, after which the yarn is in the front of the work from having worked the purl stitches. YO the needle stopping at the back of the work to set up for the SSK. It is not necessary to bring the yarn all the way back to the front of the work this will put the yarn in the wrong position to begin the SSK. It will feel like the YO is incomplete but if you look at the needles you will see that one stitch has been added. Here is video demonstration:
ROW 3 DEMO VIDEO

Grafting/Kitchener Stitch
This block is worked in two pieces that are not bound off. Instead, the live stitches are grafted together. The technique used is Kitchener Stitch, which you may be familiar with if you have ever closed the toe of socks. Grafting allows for symmetry of the lace in Pattern A. There are two types of grafting; grafting in garter is used for each vertical edge and grafting in stockinette is used for grafting the main body of the block. This video explains how the grafting is done for this block:
GRAFTING/KITCHENER STITCH VIDEO

I really don’t want to have to graft—what else can be done?

If you want your block to match the picture you will need to work the pattern in two pieces and graft them together as described in the pattern. Grafting allows for the symmetry of the upper and lower halves of the block. One could modify the pattern to work the entire block in one piece, however this would result in a loss of symmetry between the upper and lower halves. One idea to modify would be to work the garter edge, then Pattern A rows 1-28, followed by Pattern B Rows 1-13, add an extra row of garter (K all sts) to put you back on the RS, then work Pattern A rows 1-28 and ending with a garter edge. The result will look different than the picture, but will have similar elements.