+1 on the posts above. as soon as i read the post i thought you should just up the number of laps on the strop and see where it gets you. for me i do 20-30 on the linen and then 50-60 on the leather before and then about 20 on the leather after though it isn't essential.

as far as touching up the blade goes, check out the chinese 12k or i think the yellow coticule without slurry will work also though isn't as high grit (i could be wrong though). i have a 12k chinese and it works good on my carbon blades but the one stainless puma i have doesn't react well to it, though i might just need to refine my technique. i have a CrOx strop that i use a lot but only for getting the shaves to be smoother, not really as a touch up (the CrOx seems too fine), i think a pasted paddle strop would be more suited for the coarser grit pastes.

it really isn't all that complicated but educating yourself on the different types of hones and strops is your best bet to decide which one is best. because really there are many different ways you can do the same thing.