Alex, use hard papers with surface sizing to minimize stain, plus, use a more dilute toner; 25g in 200ml water is pretty strong - I was mixing my tannic acid toner by putting 1 dessert spoon into 1000ml only! You don't need to see the result "in the toner", 5 to 10 minutes toning is plenty enough; the print will darken considerably while drying. You'll experience less stain if you keep your toning times as short as possible.
Also, it's crucial to process well the paper before toning. You have to clear iron from the whites completely; do normal development then use a citric acid or Na2.EDTA or Na4.EDTA + citric acid (target pH 3-4) clearing bath to eliminate all iron from your paper to protect the whites. If not, you'll get extra stained highlights. (In every parts of the paper where the sensitizer was applied - actually...)
The toner solution keeps for months IME, I was occasionally filtering it to clear debris and such.
BTW, tannic acid / tannin toning works well with both Trad. Cyanotype and New Cyanotype.
Hope this helps,
Loris.