Just to add in some additional information to the way in which the lime works with clay, it also changes the structure of the clay which in turn effects the plastic limit. The plastic limit is simply the moisture content at which the clay becomes wet enough to act plasticly, by adding lime, this increases the moisture content at which this happens.The result of this is the point at which the clay becomes too soft and wet to be handled increases, so not only do you remove some water(heat of hydration) you increase how wet the soil can be to be used. Therefore there are several distinctive process which all 'improve' the soil. Also if you keep adding lime, the clay minerals start to break down and the silica and alluminum in the clay combine with the water and calcium (from the lime) to form cementitious materials [calcium alluminate hydrate and calcium silica hydrate]. It sounds like what you only need to achieve is an improvement in the soil by reducing the moisture, but there are also beneficial side effects which can improve the soil above and beyond the same soil if was only dried.
I have written a presentation in microsoft powerpoint on how this all works, and will send you a copy if you are interested, but I will probably have to generate this as a .pdf due to its size, sorry but the animation wont work. (contact me at ian@geotechnical.co.uk)
As to the effect of the lime clouds, this is a VERY serious issue, yes it is normally quicklime that is used, as this is the most reactive, and you should assess all the risks involved with this. Suitable protective clothing, such as masks, goggles and gloves should all be available.
Approaching people from agriculture to help is a very sensible solution, in the UK we have found that there is some cross-over between the two sectors, and often they have plant and equipment which although designed for farming, works very well on construction sites.
There is also specialist plant availble which rotovates, mixes and blends the lime within a hopper to prevent problems with lime dust, and this also includes much smaller plant suitable for single track roads. Whether or not this currently available to you, unfortunatley I cannot comment, wrong side of the world sorry.
If you wont to have a look at some of the kit available, companies in the UK who specialise in this are people like Powerbetter, Con-form, Beaches, Geo-firma, Stabilised Pavments, O'keefe Soil remidiation etc... all have their own web-sites.