2nd Log looks decent. I dont see anything wildly alarming yet on it. The first one looks similiar to an issue i dealt with with boost overshooting, then undershooting, then overshooting again and again until it hit target boost.
In my experiences with working out boost surging and spikes, it ended up being an overly sensitive turbo-dynamics table(s). The numbers were set too high for correction, so on cold mornings, boost would often overshoot its target, then it would cut the wastegate back too much, it would undershoot, then it would increase the wastegate again, causing an overshoot, and would repeat itself over and over.
The way my tuner and i approached it was by Zero'ing out all the TD tables, and starting from scratch by setting one set Wastegate duty cycle number for the car to achieve, and worked around getting a number that reached our target boost, as if it were a manual controller (say, 55% for the whole high WGDC table). Once we found a number that got to our target boost (letting it taper off by redline), we slowly worked in the TD table corrections bit by bit until it no longer would cause surging or overboosting on cold mornings. It took a few trys before we got it down pat, but i hope this process will help you at least get to a starting point if it is infact a tuning issue, and not mechanical.