Mixing fresh green grass clppings in will cause it to heat up and kill the worms. I would probably opt for useing it as is.
You also could keep it damp and let the worms finish it up.

How long it takes the material in a compost pile to finish composting depends on many things starting with what is in the mix to start, the size of the material, the Carbon to Nitrogen ratio, and the moisture. Too much moisture will slow things down as will too little moisture. If your pile had been heating up but does not after turning that could be an indication of not enough Nitrogen or maybe too much water was added.

It doesn't sound like it was N-starved, just that there are occasional bits of leaves, etc. still visible. I would use it now, but what you're asking for usually takes a few more weeks or several months. Compost cooks fast at the beginning, but to get what you're looking for requires a looong tail during which things happen rather slowly. No substitute for it, despite what the sellers of 14-day compost tumblers say.

Well I suppose a little patience is in order. The piles are made of vegetable scraps, yard trimmings and mulched dead leaves btw. I gather up old leaves from the woods behind my house for the carbon and hit them with the weed whacker before they go in. The veggies also get cut up into small bits. This year is the first for me paying attention to ratios, turning and water, etc and what a difference it makes. This morning I got steam again but I guess being in the mid 80s outside helps things heat up.

Forgot to ask, would it help the almost finished pile to add in some old cow manure? It could be fresh or old and crusty. There is plenty of that around here.

Re; Cow manure. Your compost is likly weed free judging from the origional contents. The manure is high in nitrogen which will restart the compost heating , but adding cow manure (fresh,old and crusty or otherwise) will probably contain a lot of weed seed. You would also reset the clock for composting the manure and thereby delaying when it will be totaly finished.
Now,back to the unlimited supply of cow manure. It makes very good compost without other additions other than moisture.Just heap it up and keep it damp while turning same as you have been or skip the turning and get same result over a longer period.
Back to your origional question about adding manure to incomplete compost made with leaves and kitchen scraps. That is a good idea once the manure has gone through initial high heat and decompsiton kill viability of seeds. Starting with manure mixed with other material is also fine since the high heat stage will occur.
If you have room to maintain multiple piles/bins of compostiable material,that can actualy reduce time spent vs quanity of compost produced. As you found when you just let the material sit long enough without turning,it winds up fine compost. Toss every thing togeather in a "NURSE" pile as it becomes available or you can shanghai family and frinds as free labor in bringing it to the nurse pile. Continue with the two batchs as you are doing now paying attention to detail on moisture and turning while the nurse pile quitly go's about it's business with minium attention. When you are ready to start a new batch,pull material which is weeks or months along in the process from nurse pile and begain working it. There will be times when material has been in the nurse pile long enough to be finished and useably with little to no effort on your part other than gathering and moveing material to the pile.

Whether to add old animal manure to a compost pile is always a dilema because what nutrients might be in that manure will depend on how that manure was stored. If not properly stored manure can loose significant nutrients (20 to 50 percent of the N and 5 to 20 percent of the P and K) as it ages, although there may be some that refuse to believe what good research at our state universities has found.
Perhaps this tutorial may be of some help.

Here is a link that might be useful: compost tutorial

Your pile sounds fine, but if you want to reheat your pile, you can add several things, including:

used coffee grounds
animal feed
cornmeal
blood meal

If I answer the question in the subject line -- how long? -- the answer IHMO is three months to several years.

If I narrow things a bit based on your first post, say three months to a year. Can't give a more precise answer without knowing some basic facts:

1) particle size of materials
2) your understanding of carbon to nitrogen mixing
3) If you use a compost thermometer to measure core temp
4) size of pile
5) proper moisture content
etc.

It you read some of the Compost forum posts, it seems that some of the most happy composters are those who seldom/never turn their pile, and are content to wait until the material breaks down in a cold pile. Let me say that I am not one of these folks. I started out with very clayish soil, and used hot piles to generate a lot of compost in a few years.

I think one of the first questions a would-be composter should ask themselves -- am I a patient person, or a impatient person? A impatient gardener would be more inclined to use hot compost as opposed to waiting a longer period for cold compost.

Of course there are other relevant questions, such as how much compost do I need, what resources do I have, as well as local regs and neighbors.

P.S. My most 'fluffy' compost occurs when I take some pitchforks of half-done compost out of the pile, pitch them on the grass, and run the bagging mower over it. This results in a fine, light, material that seems much more 'fluffy' than my sifted compost. A favorite use is covering my lettuce and spinach seeds with this product.