I've arrived at the point where I can cut the openings between the ferns. It's just that some of the openings are so narrow that a normal angle grinder doesn't fit in between. Fortunately there are several solutions:
Both have their advantages- and disadvantages. The chainsaws can cut a very narrow and deep slot. They are 'easy’ to handle, if you leave out the weight of the machine itself. That's because the weight is pretty close to your center, and the blade is relatively light in weight. They have several drawbacks, of which the most important is that the chain wears out fairly quickly and is very pricey. Furthermore, hydraulic machines are very tiring because the hoses weigh a lot, and petrol versions smell bad and make a lot of noise. With the ICS gasoline chainsaw I've had bad experiences with the air filter becoming wet, causing the motor to choke. These older ICS ran at double oily mixed gasoline, so you inhaled a lot of smoke. Hopefully the Stihl is better. Since recently, there are also versions on 230 Volts, but they seem to have less power.
The Cut-n-break saw is designed to cut an inch or two, two and a half, at a time, and then break away the intermediate material with the supplied crowbar, after which you can continue cutting. It's a surprisingly quiet machine, and it uses very little water, but it didn't go very fast through the Dolomite stone. Probably the blades had become a bit dull, but I had no sandstone to get them sharp again. Also, it was not easy breaking away the material, this stuff is very tough; it is not a masonry block. The weight of the machine is far away from your center, so I found it very hard to cut above my head. Furthermore, it pinched rather quickly when I accidentally moved sideways a bit. The machine was otherwise very well designed, For example, the tap for the water was in an ideal spot.
I thought I'd someday buy one of those machines, but it is nice to first know how they work. I think my choice might be a chainsaw, but it is a lot cheaper to rent for the time being. (update April 2015: it's a electric stone chainsaw in the end)
I ended up cutting the top hole almost entirely with the angle grinder. With some water for cooling and lubrication it went very quickly. For the lower two holes the break saw was a terriffic solution.