I can't give you advice, or even my simple opinion, on comparing the various types of composting on your list because I haven't tried them all, or use them all. But I can give a brief overview of what I have tried. I have a 20 acre homestead farm that creates its own "fertilizer". With the addition of foraging, hunting, and trading, the farm is capable of producing the food we and our livestock need, plus a bit extra.
Hot compost: this takes the most time and labor, but it has the benefit of producing usable compost in 60 days, though I normally turn the pile an additional time then use it at 90 days. I'm creating enough compost that I don't need to rush it, plus I prefer to 90 day target because I am using livestock manure in the piles. The 90 day compost has gone through 3 heating cycles to help eliminate pathogens. I start this compost by laying "greens", "browns", manures, and a tad of old compost or garden soil to create a cubic
yard of material in a lined pallet bin. I cover the top with a sheet of cardboard to help keep out excess rain and keep an even moisture level. At 30 days the material is turned into another bin (water added if needed). At 60 days I usually turn it again into another bin (water added if needed). At 90 days it's cooled down sufficiently to use. The volume has reduced significantly by then. I use a Mantis tiller to help turn the material, then shovel it into the next box. Most of the original material had been chopped prior to going into the compost bin.
Pro-- fast results
Con-- takes labor
Cold compost: I use cold composting in areas that I'm creating for future growing of certain crops -- bananas, chaya, taro, sweet potato for leaf production, cholesterol spinach & Okinawan spinach, pineapples. It is also used for hugelpit beds, the difference being that hugelpits are a way of filling in deep holes with waste wood and thus creating non-irrigation dependent banana patches. This method is not very labor intensive and has no time schedule.....a huge benefit to me since I'm perpetually short on time. Cold composting consists of lots of layers, plus I can dig in a
bucket of whatever I need to dispose of (rotted mangos, rotting citrus, etc). It takes longer for this material to decompose, so I use this method when I don't need to plant anything for the coming year. In my climate, some of the ingredients take more than a year to decompose, such as bananas trunks & brush trimmings. Typically, not all the ingredients are chopped prior to being added, thus much of the material is coarse. In the course of creating a cold composted bed, I also layer in some shovels of soil and lava gravel & coral sand, more or less creating my own "garden soil" on location.
Pro-- low labor
Con-- takes time to mature
Chicken Sheet Mulch: I haven't tried your method, but it
should work depending upon how much material your chickens process. I use chickens are part of my fertilizer program, but the hens are penned in a stationary pen. In additional to their feed, I bring grass clippings (2 to 3 trashcanfuls) to them daily. Once a week I lightly till the pen litter. Whenever I need material to add to the hot compost bins, I harvest pen litter. My set up normally includes 60-80 hens in a 10' by 50' pen.
Pro-- produces wonderful high nitrogen material. A side benefit is eggs and meat.
Con-- some daily labor required
Worm bin: I don't have extra time on my hands, so I don't raise confined worms. Instead, I tend the worms directly in my garden soil via compost and mulch.
Pro-- grows plenty of worms to benefit the garden soil. Zero extra labor required.
Con-- cannot make worm tea, but I don't need it in my system.
Compost with herb or biodynamic additions: I don't use this method.
Bokashi: I often bury organic waste directly into the garden soil. I see no need to ferment it first. No need to capture IMO. My compost grows IMOs. Original inoculation occurred years ago and I have no need to collect IMOs for each new batch of compost. I simply add a few shovels of my garden soil or finished compost to each compost batch in order to introduce the IMOs I'm interested in.
Pro-- quick and easy way to dispose of a small amount of waste. No need to go about a fermentation process.
Con-- have to be careful not to dig it up too soon since it takes a couple of weeks to decompose. Not a good method to handle the volume of waste that I process.
The compost methods I use are tailored to my own location and climate, and availability of input materials. Plus it is dependent upon the time I have available to do it. Thus choosing a compost method is highly individualistic. As long as it is a method that is pleasing to you and it produces fertilizer, it's just fine. One method isn't superior to another if the end product works.
As for adding the chicken
tractor waste to the chicken pen, it sounds fine. The chickens will work it into their pen litter. Chickens prefer to scratch apart piles, not bare flat ground, so I will daily rake up pen litter into piles. The chickens flatten them pretty much by the next day. It's a great way to mix up the litter and keep the flooring from getting compacted.
One more comment.......I'm a believer in keeping things simple - the K.I.S.S. method. Thus I don't use all the complicated, intensive methods often talked about.