The wiping and leveling is all initiated by commands in the start gcode. You can very easily remove those commands, and then there will be no more wiping and probing (easy part). That leaves you with the hard part, which is how to level the mini build plate, and get Z=0 to be the surface.
There is no built-in manual leveling adjustments on the corners of the mini bed. You could use shims (difficult and time consuming to get right), but more practically would need to devise some kind of new adjustable mounting points for each corner.
The mini homes to Z_Max, which current firmware defines as Z=158, so moving down to Z=0 currently puts the nozzle about 3-4mm above the bed. Changing Z_Max to 161 or 162 and recompiling would make Z=0 close to the bed surface – and from there, your newly devised manual bed leveling/adjustment system would come into play in order to get the surface level and aligned at the new Z=0 point.
It might be better to fix the leveling problem. What you describe is not typical or normal behavior – the leveling is normally reliable unless something is broken or the pad is dirty.
The skipping of one or both right-hand washers is often a sign that the X-Carriage is not parallel to the bed – that is easily fixed by manually adjusting one of the threaded rods. The skipping of all washers (moving over each washer, but never probing downard) is usually an electronics problem (wiring or board). Skipping the probe sequence entirely (never moving over or probing any washers) typically only happens if there is a problem in the Gcode (although I have seen a rare, intermittent issue in the 1.1.5.xx firmware which causes that on about 1 in 20 prints – and that will be fixed in the 1.1.8.xx firmware when it is released.)
I should also mention that Lulzbot is investigating a way to save/restore the leveling data in memory. If that happens in a future firmware, then you would be able to store the results of a successful probing sequence – and simply restore it for a future print, rather than it running for every single print. No idea when (or if) that will actually be implemented.