You can certainly keep two logbooks. One as your scrapbook, log anything you want book, and another for job apps, ratings, etc.

My early log books from almost 25 years ago are all non-professional flying, and I logged everything, including notes about pax, hotels, fuel cost, maintenance issues, etc. Might even be a smiley face or two in there.

I don't really give a crap if some interviewer 3 decades later finds that not to his dainty liking for a $15,000 net pay per year regional jet job.

As to logging the technically wrong things, ya, fix that.