If you have two switches and two floats, the high set likely triggers the alarm, the lower group sets the heating element off by cutting power to the pstat.
Each switch probably has two ~6" lengths of wire with male spades. Working with the "high" switch, connect the machine's wires leading to it to each other with a homemade "jumper" - 6" of wire and two male spades. This SHOULD silence the alarm and we can go from there.
By grounding the boiler level probe wire, do you mean unplug it from the boiler end of the wire and just touch it to the frame somewhere?
Yes - note that the boiler end of that wire is a female spade. In order to keep it grounded, you would need to make a jumper wire with one end attached to the machine ground and the other end having a male spade. But I think we are beyond that now, especially if your water reservoir has two floats and your reservoir support has two switches.