DESPERATE for Workaround to the 1 SAVE ONLY Problem
This post only refers to Community Maps. Unfortunately, unlike bsp files that allow unlimited Saves . . . the Community maps only allow a single SAVE. ACTUALLY the single Save vanishes when you start a new map - so you really cannot even save a single snapshot of "where you were".
This is all I need - one SAVE per Map so that I can play several maps and pick up where I left off. I want to store my progress . . . switch around . . and play other maps. But no. The current Map Save is overwritten as soon as a new map is started. I cannot believe they spent years developing this software and FORGOT to allow Saves. WHAT WAS VALVE THINKING ??
Since the Saves are stored on a Host there may be no workaround.
If there was a way to store the Save's locally . . . then that might work.
Does anyone know if this is possible ? TIA
PCDoc, there is an easy and quick workaround to circunvent this limitation: play the map via the console 
Just find the puzzle you are playing into your maps/workshop/[long_number_named_folder_here] folder (it might have a number-name), note its name and type "map map_name_here" into the developer console. If that wouldn't work because of being under /workshop/[whatever_number] folder and not directly into your /maps folder, just ccopy it in to your /maps folder and you're done.
useful tools and stuff here on TWP 
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You can also just add workshop/ onto the map name.
Have you tried map_wants_save_disable 0? That might allow more saves.
Geniuses . . . sheer GENIUSES ! !
Thanks so much. I am beside myself . .
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ADDENDUM: actually it is harder than I thought, to do this because none of my Maps are "Named" by their names in the Workshop folder.
For example, I am playing Azorea's "Attunement" and it is not listed anywhere. So here is what I needed to do
1) I found the "map ID" by going to Steam, entering the Workshop View and it shows the "ID" of the map in the URL at the top. The ID was 107880965
2) I then searched all the Workshop folders for that ID and found a match in a file under a folder named: 937008435250144772
3) in that folder is a file called: "thumb107880965.jpg"
Which has the map ID of 107880965 in the filename.
4) however, it is a thumbnail jpg, not a bsp file.
Luckily - in the same folder I found a file named: 1352676344.bsp
And that IS Attunement !!
5) I tried entering: map 1352676344.bsp
In the Console - to no avail.
6) I renamed it to "Attunement.bsp" and copied that to my "Maps" folder.
Finally it played - whew !!
It needs to be renamed because I will never remember which map it is otherwise when I pull up all my Saves. To be honest, I was hoping for an easier way, but this is better than not being able to Save the maps. I have not tried the Console command for increasing the number of Saves but that does not seem to be the problem here.
They sure make you jump through some hoops.
I'm a little late with a reply, but it seems to me there is a much simpler way to do this.
The "1 save only" limitation is only if you use quicksaves.
When playing ANY map, use the console to save and load.
To save, type: save filename
where "filename" can be any name of your choice, but ideally uses the map name. Multiple saves are allowed, eg "attunement1", attunement2", etc. Note that it won't warn you if you use an existing filename, so be careful not to overwrite a save that you want to keep.
To load, type: load filename
the console includes a convenient search-as-you-type function, so if you type "load a", but not press enter, a list of all saved files starting with "a" will be listed - scroll down to your choice and then press enter.
It works whether the map is opened from the community chamber menu, or via the console using the bsp filename. The savefiles are stored locally, and uploaded to the cloud when the game is closed.
Wow man, good to know! 
useful tools and stuff here on TWP [spoiler]
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Looking at this thread it didn't even occur to me to do that, even though I used to do that sort of thing in Skyrim/Oblivion all the time to get custom-named saves.