What should I do about my rendering & damp-proof course?
A drop of 150mm would work best if you did it in the summer so that the bricks below the DPC could dry out a bit.  If you did it mid winter and another big freeze happened then these bricks could be subject to freezing and surface cracking / erosion.  In general - if you do drop the garden by 150mm the bricks below the DPC would benefit from some form of localized rain and wind protection because of the age of the building.

If the garden slopes toward the building or the water table is quite high in your area it would be essential to make sure that any moisture in the garden is diverted away from the building via good drainage such as a French Drain.

There are one or two ways in my experience to tidy up the brickwork below the DPC :

1 : brick slips (slices of new brick) on a fascia with an inch or so of breathing space behind it could be painted to match the building without permanently affecting or altering the original bricks below the DPC.  This would still need a bit of venting.

2 : wooden skirting, a bit like an external skirting board (in period with the building) painted to match might be cheaper and easier to install.