If you google it you will see a couple tour operators. Prices are quite high but I doubt there are cheaper options, I found most tours in Laos to be expensive and they almost never group you with other people to reduce costs.
Not sure where all you are travelling but if you are going to Vietnam make sure you see Paradise Cave. I can't say definitively but I am pretty sure it is nicer then Chom Ong, it was one of my trips highlights.
No I had looked into doing so but financially it made no sense especially since I was a solo traveller.
Here is a report of someone who did it without tour. Doesn't mention costs or all that much detail about how to do it.
If you are really set on going and don't want to pay tour prices then something like he did is likely your only opportunity. I found Laos makes it very difficult to try and experience things like this on your own, it was really hard to get reliable information I think because they want you to pay their outrageous tour prices.
I exchanged few emails with this guy and he spent just ouple hours inside the cave, so I am afraid that something like that will not justify a flight from Vientanne and then backtracking to LP.
thanks for the help