I just thought of a neat idea for pyraBLD. Perhaps this has already been tried. Inspired by the U-method for 2x2x2 BLD you could use the turning to realign the centers to do the edge three cycles.
For example, say the U center/tip has to turn once clockwise to be aligned as in the solved state. You could take three edges in your memo that have to 3-cycle and do an extended sequence of setup turns to set them all up to the U layer such that doing the U turn to align the center/tip
also does the three cycle of edges. Then you reverse the setup move sequence to put the three edges back to their original positions. This will typically solve two edges, and put a new edge into your buffer edge position.
Repeat the process for the next center/tip and the next three edges in your memo. If you run out of edges in your memo, then this means the edges are solved but perhaps some center/tips are unsolved. In this case you would rotate those center tips by themselves using the process I described in my earlier post in this thread.
If your center/tips solve before you finish solving the edges, then you can solve the remaining edges using commutator 3-cycles as normal.
I think with practice that this method may be even faster than the "standard" BLD approach because of the significantly reduced overall move count. I may give this method a shot

I've tried the U-method on 2x2x2BLD, but never its equivalent on pyraBLD.
That may be another method you would be interested in.
Nice
For expert pyra solvers this would probably be the fastest way, assuming a 1 look style method is reliably "easy" without taking too long to memo. I imagine 1 look would be possible for a pro pyra solver.
For the non-pro pyra solvers, the BLD based methods I listed may be good options to get to intermediate level speed on pyraBLD