You need both bar tape and grips? My Jones H Loop bars have both, but that is quite unusual. The Jones bars are funky.
What speed is the bike? 8 speed?
I'm 5'7", and yes, it's easy to find bikes that fit, I have long arms and legs, and can ride both men's and women's, typically. I wear either large or extra large women's cycling gloves, maybe a medium in mens (I have some extra size large women's, I used to like them tighter than now. Shrug). Wear size 10.5 street shoes, but in cycling shoes something like 43.5 or 44, clipping in requires toe room. I may have some extra stuff lying around that would fit you. My feet and hands are really large for my height. (My sister is 6 feet tall, and wears women's size 12 shoes, minimum). I'm the runt. The Bontrager SPD shoes I have that don't work for me are size 43, though, and a bit too small. So probably would be for you, too, unless you have very small feet and hands for your height.
My Trek 7200 is a tad on the large size. I can make it work by adjusting the adjustable stem so the bars raise up and towards the rider. I think it's a size 19 or 21, can't remember. Anyway. That's why I was asking what part of the country you are in. (I'm not far from Savannah, GA. About 50 miles). An inexpensive bike isn't worth shipping. Costs too much.
What kind of touring bars were you thinking? Drop bars would require a lot more parts and money.