Years ago I made up this money clip using laser cut timber inlays

However, befor resorting to inlays I engraved the "K" to a depth of about 2mm and backfilled with Jarrah coloured Timbermate.  I then tried to "over engrave" with the "A" to infill with pine colour...  there was no issue engraving the base around the original "K", however with the Timbermate backfill, the 2 passes (to get 2mm depth) didn't even char the Jarrah Timbermate.
I'm hoping that there may be some other product that may permit the backfill to be engraved to some depth... even it it was 0.5-1.0mm, enough to lay some stuff in the "over engraving".

If your first cut is too short... Take the second cut from the longer end... LBD