Maybe I missed it amidst all of the grammar scolding. What is your headroom in this building? I think micro piles are your best bet here. a lo-drill or similar machine is going to be to wide or too tall for most building access. There are quite a few small bore drill rigs that can do micro piles...
There are small vibratory drivers/extractors made specifically for driving and extracting vinyl and aluminum sheet piling. Here is one example. http://iceusa.com/pdf%20files/vibrators/2-50-10Jul07.pdf
In the past, vinyl sheeting was thin and flimsy. It would deflect if it hit any obstruction...
What about de-watering with a wick drain material. Here is a company that makes wick drains and specificaly the different styles of drain.
http://www.americanwick.com/applications/detail.cfm?app_id=15&app_cat_id=7
The ICE 223 vibro is a high frequency vibro that was designed to excell in sandy/ silty soils. The 223 is a high speed version of the standard frequency model 216. I have personaly witnessed these two hammers used on the same jobsite with an amazing difference in performance. The contractor was...
Wow, thats a big hole. You should be fine. It is normal to displace water in a cast in situ piling this way. The biggest problem is going to be sinking the cage through the aggregate. Normaly you would use a grout instead of concrete in this situation. Grout uses more sand instead of aggregate...
Micro piles...maybe. Why not cast in sitiu piling? You would be able to install a much smaller # of piling although the grout costs will be higher than micr but cheaper than driven.
It sounds as if these timber piles are structural in nature. If that is the case, the minimum tip is only part of the equation. You may be able to calculate the hoe as a static test but the figure will be a SWAG. If the contarctor insists on using the excavator he could use something similar to...