I'm about your size (inseam is the same) and have had the same problem. My bike came with a Sargent - and I found it surprisingly hard and comfortable (yes - comfortable). As Dave said though, it is wider and you need longer legs....
The problem with the ST (view from my height) is when stopping out in the real world. You see, the roads are not always flat and level, and if I stopped over a dip, pothole, or an off camber turn, my legs are just not long enough to prevent that dreaded and embarrassing tip over. I considered ballet lessons but decided doing en pointe practice was too hard on my toes. Seriously, I went the Spencer route, and did not find it unduly uncomfortable. The problem with lowering the seat is the seat pan. There is only so much foam that the maker can remove before he runs out of space. I don't think aftermarket seats are going to be much lower - even if customized for a short rider. But, all in all, the Spencer option will give you maybe 1" and is a cheap mod (certainly better than a RDL seat that could easily set you back close to a thousand for both seats).
Lowering the chassis did not warm the cockles of my heart. It would make the bike more difficult to sell, possibly change the handling (esp two up), and adversely affect the geometry of the center and side stands. Yes, you can cut and shorten the two stands if you lower the suspension, but it adds another layer of cost. I gave up on this idea pretty quickly and have learned to live with the bike. Oh, yes, I did get new boots (more or less standard height, but they added maybe 1/2") and I wear thick socks.
If you have difficulty getting the bike up on the center stand, PM me. There is a fix for this - sort of.