You need to wait until the stalk on the fruit goes brown. Even then you can leave them on the vine longer, especially until after the first frost hits the vine. This will mature them and make them sweeter.
When you pick them, cut off the stalk as long as possible (2 or 3"), and leave them in the sun for a few days and they'll store better.
If they're already 10" and fat you have a bumper crop on the way. Well done.
(Just take a look underneath them occassionally while they are ripening and ensure no critters are burrowing into or under them. If so, a piece of board or something to hold them up off the soil may help.

* * * *

The secret is the soil.

I planted a ba~zillion of those too...
By accident..
Left one little squash on top of the soil
in the fall time.. and now I have sooooo many
baby volunteers, I'm giving them away to neighbors and 4~H Junior Master Gardener groups..

I always thought the color on the outside
was more of a tan or buttercreme like... instead of orange...

* * * *
Weezie

Don't forget to be kind to strangers. For some who have
done this have entertained angels without realizing it.
- Bible - Hebrews 13:2





http://photobucket.com/albums/y250/weezie13/

I haven't ever intentionally tried it.. but I do know that some of the hybrids' out there do not come back or grow true to seed... they are hybridized from two kinds and mixed and matched and when pollenated they can revert back to one of the parents....

But hey, if you love them and enjoy most of them,
why not try it, and see what happens..

Like I said for mine, I just left the darn thing on top of the soil/dirt and it broke down over winter and seeded it'self in the spring..

NO work at all on my end..

* * * *
Weezie

Don't forget to be kind to strangers. For some who have
done this have entertained angels without realizing it.
- Bible - Hebrews 13:2





http://photobucket.com/albums/y250/weezie13/

That I am a sucker for...
I love anything that grows..
and have a hard time telling a poor little plant it can't grow... especiallyyyyyy if it's lasted the whole winter long and then to sprout in the spring time..

*I have a hard time YANKING the 100+ volunteer tomato plants I get every year, that I have nooooooo place to grow...*

I agree with what you said...
And I also believe whole heartedly on a seed that reseeds it'self to be stronger and more resistant to things when naturally self~seeded..
than when we plant them and choose thier spot..

I do have problems with my tomatoes, that septoria wilt, and it's everywhere...
So, it sometimes almost doesn't matter where I put them.. it's already there..

But I think you have to know your garden, soil, etc.. and be reasonable content with what you know, how much garden area you have, and what you can put where..

I do alot of rotation, when I actually plant..
but when it reseeds it's self, I tend to be too soft hearted..

*that's what takes me so long to plant my garden sometimes, I have to remember what I had growing one year, and what I want to plant this year, and if it's in the same family or same bug attracker.. and I am on limited space believe it or not..

The part I had for my corn last year, which was all manured up good for corn, I was going to put tomatoes and lettuce.. buttttttt, "The best laid plans of mice and men" that darn ole squash had other ideas..
(*oh, did I forget to put that, I had picked up the squash and put it down there, and forgot to do anything with it..*)

I even had cantaloupes re~seed and sunflowers, and watermelons..
I gotta stop leavin' those things around...
Heck, they even reseed in my compost pile..
*(when I open like an acorn squash and pull the seeds out and throw them into the pile..)*

* * * *
Weezie

Don't forget to be kind to strangers. For some who have
done this have entertained angels without realizing it.
- Bible - Hebrews 13:2





http://photobucket.com/albums/y250/weezie13/

Oh my, I gave that up about the 3rd year I had my back perennial bed...
I had a raised bed, 60ft long, it was 4 and 8ft wide, at certain points... I made stone path way to walk in the middle and had assorted bulbs and columbines and snowdrops, and all sorts of things, picture perfect..
The 3rd year came and all h#ll broke loose..
Columbines where planting themselves in the front, bulbs were all over the place, and the plan when to the wind, literally...
I have since learned NOT to drive myself crazy,
and that Mother Nature's got a pretty good eye...
*(and less work)

* * * *
Weezie

Don't forget to be kind to strangers. For some who have
done this have entertained angels without realizing it.
- Bible - Hebrews 13:2





http://photobucket.com/albums/y250/weezie13/

The one you have already cut is toast.
The other two may be OK if you just leave them until they colour up. It may take months so be patient.

* * * *

The secret is the soil.