worm watering

So, the idea behind this is I have different gardens around town i manage their organic food gardens. I have been using water that i pour through my worm bin, then haul around to the gardens i'm doing maintenance visits for in 5 gallon buckets. I do this about once a month. -i just pour 4-5 gallons through the worm bin, then mix it all together and use it all that day. I dilute it a little bit at the different properties. It's easier than harvesting worm castings, better than leachate, and easier than bubbling worm tea.
But it's time consuming and laborious, So I'm trying to stream line that at a few gardens. As well as give clients a place to put their food scraps. I need others to point out things i'm not thinking about or any blaring problems with this idea. It may not be original, but i have not seen it before. My first tests site will be at a gym, so we're hoping to have members coming in bringing their kitchen scraps, and feeding a few 15-gal size worm bins. but the garden is small scale- about 250 square feet, so i won't need a ton of worm tea.

The idea:
60 gal rain barrel, elevated to about 5'. That is connected, via spigot to 1/2" poly that runs to a greenhouse mister type fitting over the worm bin- worm bin is elevated about 3'-4'... i've thought i might just use a garden hose fixed to a nursery nozzle... the point is to spread the water over the surface of the worm bin... Then when i turn on that water, every few weeks, it sprinkles gently through the worm bin. The water filters through the worm castings in the worm bin, collecting all of the worm poo goodness, then goes through another bin that has a screen to catch any worms or debris that falls through. Then the water goes into a 3rd container (they're all stacked like a typical homemade worm bin), that will fill up 6-7 gallons. Attached to the 3rd collection bin will be my hose that i can just use to water the garden. The point is to keep pressure by having that reservoir, and as long as the amount of input water is roughly the same as output water, the pressure will remain roughly constant. I love my wife.

My main concerns- will 5 gallons elevated at 3', though a garden hose, be enough pressure to reach roughly 75'? I guess it doesn't have to be very high pressure though... how would i go about figuring that out? Do y'all think this will work? How much pressure will i need going into the worm bin to get good coverage though one of those overhead misters? It is a lot of plastic, but i'm trying to provide a place for food scraps as well as use worm water for the garden. Any better ideas?

If anything is confusing or incomplete i can go into more detail.

The quick answer is yes, the water should reach your destination, and the pressure you get will depends in large part on the diameter of the pipe/hose/tube you run, and the 'fullness' of the upper tank of water.

Assuming an ideal fluid, you'd use Bernoulli's principle to calculate your downstream pressure:

P1 ​+ 1/2​ρ[(v1)^2]​ + ρgh1 ​= P2​ + 1/2ρ[(v2)^2] ​+ ρgh2
Learn more here:
https://www.khanacademy.org/science/physics/fluids/fluid-dynamics/a/what-is-bernoullis-equation

P1 and P2 will be the same, because you've got atmospheric pressure at both ends of this thing, and since we're recklessly simplifying stuff, we should just call the initial velocity (v1) zero as well, because your reservoir is large enough.
That means your pressure in this system is coming from h1, your hydraulic head. More height difference between the sprayer and the top of the water in the big tank = better pressure.

The hose size piece of this puzzle has to do with Poiseuille's Law (pronounced: P-wah-z-eh?). Details spared here; bigger diameter is better, longer run is worse. [don't go there with the joke]

That's the rough fluid dynamics of the situation, but as always, prototype it out at home before you build it on site

...and after rereading what i wrote, i found out my wife typed in a little something extra in the description when i was cooking... sneaky sneaky

Sneaky wifey!  Don't you hate it when they do that?  

I'm thinking if you have 2 feet of vertical between the rain barrel and the mister system, the mister won't work well.  I presume they need at least 5, or more likely 15 psi to squirt properly.  To get 1psi you need around 2.5 feet of head.  Could you just drill/poke holes in the poly to do crude sprinkling on top of the worms instead of the misting?  My husband's a dumbass.

Regarding getting the water to move 75' in a garden hose from the lower tank to the garden, that should work but it may come out rather lazily.  And if you hold the hose a foot off the ground it will be much more lazy than if you had it on the ground.  Surprisingly, it doesn't matter if you have 5 gallons or 500 gallons, if there is 3' of head you'll have a touch over 1psi of pressure.  Then the resistance to flow of the garden hose will be the limiter.  Bigger hose diameter is better.  Spray fitting on the end is too much resistance.

I'd probably just go from the spigot into a 2.5 gallon watering can and carry it to the garden to hand apply.

I don't think you need misters.   I've got worms in a blackwater tank, the water from a flush toilet enters it through a 3" pipe coming from the house through the top of the box, flows through the box/tank on a slight slope, and leaves by a 2" pipe on the bottom edge of the box/tank, through a gabion of 1 1/2" rocks in a double chickwire cage, flows out into a secondary box where the castings can be scooped out, and runaway worms can be put back.  

It's a low-flow toilet, approx. 1.5 gallons per flush, the worms are perfectly happy.   As long as the line doesn't plug up, which is hasn't in the year I've been using it, or they freeze or they bake.  A protected box seems to handle that well in my mild-winter zone.  

The diagram should have the box/tank on a slope, but I'm not that much of an artist.

thank you all for your input!
I think instead of a mister i'll go with the jerry rigged type drip system, i don't think a mister would be best for this anyway now that i'v been able to think about this idea for more than an hour. I'll be decrease the height distance between the rain barrel and the worm bin, to slow the drip into the worm bin, i'll go with just poking holes in the poly. And i'll increase the height of the worm bin... although it may be beneficial to have slow output. I'm thinking i could just drop the hose end at the base of a tree while checking on it or doing any other short tasks. I'll just have to work out any kinks or problems as i build my first one.