I believe that my Stans syringe has a plastic tube which fits over the valve body. With the valve at 6 o'clock, with the core removed, I can't imagine how you could remove most of the pooled sealant. Wouldn't you get mostly air?
BTW, I've been riding my regular road bike for several weeks to prepare for a 100 mile 1 day ride up in NH's White Mountains which I finished last Sat. 6,000 ft of ascent. Lots of fun, and we raised a lot of money for a handicapped cycling program I do volunteer work for. I looked at my neglected GG bike this morning, and the front tire was totally flat. No visible sealant leakage. I pumped the tire up and it held air and pressure. Does this mean it's time to refresh sealant? If so, how much should I add? They are 40 mm Rambler TR's. When first mounted, I used 2 oz. of Orange seal in each tire.
To ADD sealant, not remove it.
I want the tire beads to be completely seated before I add any sealant. Much easier and cleaner than trying to refit a bead with sealant sloshing around, and it may not reseat easily when you try to inflate it.
Generally, if my tires are losing significant pressure over a couple of days I will add 20-30ml.