How much cycling time?

Ok everything that is in the 55 gallon has almost been in it a year (sand, plants etc). My plans was to do this:
Remove half the sand from the 55 (there is a lot), the drift wood, plants, clay pots and about 3/4 of the water and put it in the 175 gallon along with more sand of course. Maybe even lay one of the used filters from the 55 in on top of the bio balls to help transfer some bacteria
On the 55 gallon I am going Africans so I guess I need to get some coral sand (??) and mix in with the sand that I leave in there or will go straight LPS if you guys think some Hole Rock will do the trick.
My main question is how long do you think each of these tanks will need to cycle before adding anything? And will the 55 really even need to cycle changing it from soft water to hard water? I was going to leave my current stock in the 55 till the 176 has cycled. I would think this would be safe because I am still leave some sand and the water I would be taking would the same as a 75% water change.
Sorry so long but wanted to try and make it clear what I was doing. Thank you for any help :-)

I think If you split the material and put half in each tank and add a few fish right away you will be fine, just add the other fish slowly, like 3-4" of fish a week.

use regular sand and either add some crushed coral, some shells or some holey rock and you wont need the coral sand.

Thank you so much Fern! Crush coral I have direct access to, coral sand I would have to order. Following your directions I should have the 55 empty of fish in about 3 weeks and then I can start setting up for the Africans. I am really getting excited about this if you couldn't tell lol

Just keep fish or an ammonia source in each tank while your working on them, no more than 6 hours without fish or your bacteria will begin to die.
5-10lbs of crushed coral should be all you need to start with. But you will have to watch the grain size and when it gets to 1/2 size add a few more pounds of it.

Glad you told me that one, I never thought of it starting to die off but without a source it would. I have a few platies I can toss in there right away, my daughter has a tank full of them in her room so if I lose some it would be sad but not a $ loss.

they would work, its fine to have fish in the tanks when you are redoing them. Also puts some of the old water in both tanks, it will have some gobbledygook in there for the bacteria to eat.

Fern has you covered. Good Luck! Sounds like a fun project!